Exhibit 4.1


 


WARRANT AGREEMENT


 


THIS WARRANT AGREEMENT (this
“Agreement”), dated as of July 26, 2021, is by and between Alpha Healthcare Acquisition Corp. III, a Delaware
corporation (the “Company”), and Continental Stock Transfer & Trust Company, a New York corporation, as
warrant agent (in such capacity, the “Warrant Agent”, and also referred to herein as the “Transfer
Agent”).


 


WHEREAS, the Company is engaged
in an initial public offering (the “Offering”) of units of the Company’s equity securities, each such
unit comprised of one share of Class A common stock of the Company, par value $0.0001 per share (“Common Stock”),
and one-fourth of one redeemable Public Warrant (as defined below) (the “Units”) and, in connection therewith,
has determined to issue and deliver up to 3,750,000 warrants (or up to 4,312,500 warrants to the extent the Over-allotment Option (as
defined below) is exercised) to public investors in the Offering (the “Public Warrants”, and together with the
Private Placement Warrants (as defined below), the “Warrants”);


 


WHEREAS, the Company has entered
into that certain Private Placement Units Purchase Agreement (the “Private Placement Units Purchase Agreement”)
with AHAC Sponsor III LLC, a Delaware limited liability company (the “Sponsor”), pursuant to which the Sponsor
agreed to purchase an aggregate of up to 455,000 units (or up to 500,000 units to the extent the Over-allotment Option is exercised) simultaneously
with the closing of the Offering (and the closing of the Over-allotment Option, if applicable) (the “Private Placement Units”)
at a purchase price of $10.00 per Private Placement Unit.


 


WHEREAS, each Private Placement
Unit consists of one share of Common Stock (each a “Private Placement Share” and collectively the “Private
Placement Shares”) and one-fourth of one redeemable warrant bearing the legend set forth in Exhibit B hereto (each
a “Private Placement Warrant” and collectively the “Private Placement Warrants”).


 


WHEREAS, in order to finance
the Company’s transaction costs in connection with an intended initial Business Combination (as defined below), the Sponsor or an
affiliate of the Sponsor or the Company’s officers and directors may, but are not obligated to, loan to the Company funds as the
Company may require, of which up to $1,500,000 of such loans may be convertible into up to an additional 150,000 Private Placement Units
at a price of $10.00 per Private Placement Unit;


 


WHEREAS, the Company has filed
with the Securities and Exchange Commission (the “Commission”) a registration statement on Form S-1, File No.
333   , and prospectus (the “Prospectus”),
for the registration, under the Securities Act of 1933, as amended (the “Securities Act”), of the Units, the
Public Warrants and the Common Stock included in the Units;


 


WHEREAS, each whole Warrant
entitles the holder thereof to purchase one share of Common Stock for $11.50 per whole share, subject to adjustment as described herein.
Only whole Warrants are exercisable. A holder of the Public Warrants will not be able to exercise any fraction of a Warrant;


 


WHEREAS, the Company desires
the Warrant Agent to act on behalf of the Company, and the Warrant Agent is willing to so act, in connection with the issuance, registration,
transfer, exchange, redemption and exercise of the Warrants;


 


WHEREAS, the Company desires
to provide for the form and provisions of the Warrants, the terms upon which they shall be issued and exercised, and the respective rights,
limitation of rights, and immunities of the Company, the Warrant Agent, and the holders of the Warrants; and


 






     


     


    

 


WHEREAS, all acts and things
have been done and performed which are necessary to make the Warrants, when executed on behalf of the Company and countersigned by or
on behalf of the Warrant Agent, as provided herein, the valid, binding and legal obligations of the Company, and to authorize the execution
and delivery of this Agreement.


 


NOW, THEREFORE, in consideration
of the mutual agreements herein contained, the parties hereto agree as follows:


 


1. Appointment
of Warrant Agent. The Company hereby appoints the Warrant Agent to act as agent for the Company for the Warrants, and the Warrant
Agent hereby accepts such appointment and agrees to perform the same in accordance with the terms and conditions set forth in this Agreement.


 


2. Warrants.


 


2.1 Form
of Warrant. Each Warrant shall be issued in registered form only, and, if a physical certificate is issued, shall be in substantially
the form of Exhibit A hereto, the provisions of which are incorporated herein and shall be signed by, or bear the facsimile
signature of, the Chairman of the Board, President, Chief Executive Officer, Chief Financial Officer, Secretary or other principal officer
of the Company. In the event the person whose facsimile signature has been placed upon any Warrant shall have ceased to serve in the capacity
in which such person signed the Warrant before such Warrant is issued, it may be issued with the same effect as if he or she had not ceased
to be such at the date of issuance. All of the Public Warrants shall initially be represented by one or more book-entry certificates (each,
a “Book-Entry Warrant Certificate”).


 


2.2 Effect
of Countersignature. If a physical certificate is issued, unless and until countersigned by the Warrant Agent pursuant to this Agreement,
a Warrant certificate shall be invalid and of no effect and may not be exercised by the holder thereof.


 


2.3 Registration.


 


2.3.1 Warrant
Register. The Warrant Agent shall maintain books (the “Warrant Register”) for the registration of original
issuance and the registration of transfer of the Warrants. Upon the initial issuance of the Warrants, the Warrant Agent shall issue and
register the Warrants in the names of the respective holders thereof in such denominations and otherwise in accordance with instructions
delivered to the Warrant Agent by the Company. All of the Public Warrants shall initially be represented by one or more Book-Entry Warrant
Certificates deposited with The Depository Trust Company (the “Depositary”) and registered in the name of Cede
& Co., a nominee of the Depositary. Ownership of beneficial interests in the Public Warrants shall be shown on, and the transfer of
such ownership shall be effected through, records maintained by (i) the Depositary or its nominee for each Book-Entry Warrant Certificate,
or (ii) institutions that have accounts with the Depositary (each such institution, with respect to a Warrant in its account, a “Participant”).


 


If the Depositary subsequently
ceases to make its book-entry settlement system available for the Public Warrants, the Company may instruct the Warrant Agent regarding
making other arrangements for book-entry settlement. In the event that the Public Warrants are not eligible for, or it is no longer necessary
to have the Public Warrants available in, book-entry form, the Warrant Agent shall provide written instructions to the Depositary to deliver
to the Warrant Agent for cancellation each Book-Entry Warrant Certificate, and the Company shall instruct the Warrant Agent to deliver
to the Depositary definitive certificates in physical form evidencing such Warrants (“Definitive Warrant Certificate”).
Such Definitive Warrant Certificate shall be in the form annexed hereto as Exhibit A, with appropriate insertions, modifications
and omissions, as provided above.


 






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2.3.2 Registered
Holder. Prior to due presentment for registration of transfer of any Warrant, the Company and the Warrant Agent may deem and treat
the person in whose name such Warrant is registered in the Warrant Register (the “Registered Holder”) as the
absolute owner of such Warrant and of each Warrant represented thereby (notwithstanding any notation of ownership or other writing on
a Definitive Warrant Certificate made by anyone other than the Company or the Warrant Agent), for the purpose of any exercise thereof,
and for all other purposes, and neither the Company nor the Warrant Agent shall be affected by any notice to the contrary.


 


2.4 Detachability
of Warrants. The Common Stock and Public Warrants comprising the Units shall begin separate trading on the 52nd day following the
date of the Prospectus or, if such 52nd day is not on a day, other than a Saturday, Sunday or federal holiday, on which banks in New York
City are generally open for normal business (a “Business Day”), then on the immediately succeeding Business
Day following such date, or earlier (the “Detachment Date”) with the consent of BofA Securities, Inc. and PJT
Partners LP, as the representatives of the several underwriters, but in no event shall the Common Stock and the Public Warrants comprising
the Units be separately traded until (A) the Company has filed a current report on Form 8-K with the Commission containing an audited
balance sheet reflecting the receipt by the Company of the gross proceeds of the Offering, including the proceeds received by the Company
from the exercise by the underwriters of their right to purchase additional Units in the Offering (the “Underwriters’
Option”), if the Underwriters’ Option is exercised prior to the filing of the Form 8-K, and (B) the Company issues
a press release and files with the Commission a current report on Form 8-K announcing when such separate trading shall begin.


 


2.5 Fractional
Warrants. The Company shall not issue fractional Warrants other than as part of the Units, each of which is comprised of one share
of Common Stock and one-fourth of one Public Warrant. If, upon the detachment of Public Warrants from Units or otherwise, a holder of
Warrants would be entitled to receive a fractional Warrant, the Company shall round down to the nearest whole number of Warrants to be
issued to such holder.


 


2.6 Private
Placement Warrants and Working Capital Warrants. The Private Placement Warrants and the Working Capital Warrants shall be identical
to the Public Warrants, except that so long as they are held by the original purchasers thereof or any Permitted Transferees (as defined
below), as applicable, the Private Placement Warrants and the Working Capital Warrants may not be transferred, assigned or sold until
the date that is thirty (30) days after the completion by the Company of an initial Business Combination (as defined below); provided,
however, that the Private Placement Warrants and the Working Capital Warrants and any shares of Common Stock held by either the
original purchasers thereof or any officers or directors of the Company, or any Permitted Transferees, as applicable, and any shares of
Common Stock issued upon exercise of the Private Placement Warrants and the Working Capital Warrants may be transferred by the holders
thereof:


 


(a) to
the Company’s officers or directors, any affiliates or family members of any of the Company’s officers or directors, to the
Sponsor, any members or partners of the Sponsor or their affiliates, or any affiliates of the Sponsor;


 


(b) in
the case of an individual, by gift to a member of such individual’s immediate family or to a trust, the beneficiary of which is
a member of such individual’s immediate family, an affiliate of such individual or to a charitable organization;


 


(c) in
the case of an individual, by virtue of laws of descent and distribution upon death of such person;


 


(d) in
the case of an individual, pursuant to a qualified domestic relations order;


 


(e) by
private sales or transfers made in connection with any forward purchase agreement or similar arrangement or in connection with the consummation
of an initial Business Combination at prices no greater than the price at which the Warrants were originally purchased;


 






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(f) by
virtue of the laws of the State of Delaware or the limited liability company agreement of the Sponsor upon dissolution of the Sponsor;


 


(g) to
the Company for no value for cancellation in connection with the consummation of a Business Combination;


 


(h) in
the event of the Company’s liquidation prior to the consummation of a Business Combination; or


 


(i) in
the event that, subsequent to the consummation of a Business Combination, the Company completes a liquidation, merger, stock exchange
or other similar transaction which results in all of the Company’s stockholders having the right to exchange their shares of Common
Stock for cash, securities or other property; provided, however, that, in the case of clauses (a) through (f), these transferees
(the “Permitted Transferees”) enter into a written agreement with the Company agreeing to be bound by the transfer
restrictions in this Agreement and the other restrictions contained in the letter agreement, dated as of the date hereof, by and among
the Company, the Sponsor and the Company’s officers and directors.


 


2.7 Working
Capital Warrants. Each of the Working Capital Warrants shall be identical to the Private Placement Warrants.


 


3. Terms
and Exercise of Warrants.


 


3.1 Warrant
Price. Each Warrant shall entitle the Registered Holder thereof, subject to the provisions of such Warrant and of this Agreement,
to purchase from the Company the number of shares of Common Stock stated therein, at the price of $11.50 per share, subject to the adjustments
provided in Section 4 hereof and in the last sentence of this Section 3.1. The term “Warrant Price”
as used in this Agreement shall mean the price per share at which shares of Common Stock may be purchased at the time a Warrant is exercised.
The Company in its sole discretion may lower the Warrant Price at any time prior to the Expiration Date (as defined below) for a period
of not less than twenty (20) Business Days, provided, that the Company shall provide at least twenty (20) days prior written notice of
such reduction to Registered Holders of the Warrants and, provided further that any such reduction shall be identical among all of the
Warrants.


 


3.2 Duration
of Warrants. A Warrant may be exercised only during the period (the “Exercise Period”) commencing on the
date that is thirty (30) days after the first date on which the Company completes a merger, capital stock exchange, asset acquisition,
stock purchase, reorganization or similar business combination, involving the Company and one or more businesses (a “Business
Combination”), and terminating on the earlier to occur of: (a) at 5:00 p.m., New York City time on the date that is
five (5) years after the date on which the Company completes its initial Business Combination, (b) the liquidation of the Company,
and (c)  the Redemption Date (as defined below) as provided in Section 6.2 hereof (the “Expiration Date”);
provided, however, that the exercise of any Warrant shall be subject to the satisfaction of any applicable conditions, as
set forth in subsection 3.3.2 below, with respect to an effective registration statement. Except with respect to the right to receive
the Redemption Price (as defined below) in the event of a redemption (as set forth in Section 6 hereof), each outstanding
Warrant not exercised on or before the Expiration Date shall become void, and all rights thereunder and all rights in respect thereof
under this Agreement shall cease at 5:00 p.m. New York City time on the Expiration Date. The Company in its sole discretion may extend
the duration of the Warrants by delaying the Expiration Date; provided that the Company shall provide at least twenty (20) days
prior written notice of any such extension to Registered Holders of the Warrants and, provided further that any such extension shall be
identical in duration among all the Warrants.


 






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3.3 Exercise
of Warrants.


 


3.3.1 Payment.
Subject to the provisions of the Warrant and this Agreement, a Warrant may be exercised by the Registered Holder thereof by delivering
to the Warrant Agent at its corporate trust department (i) the Definitive Warrant Certificate evidencing the Warrants to be exercised,
or, in the case of a Book-Entry Warrant Certificate, the Warrants to be exercised (the “Book-Entry Warrants”)
on the records of the Depositary to an account of the Warrant Agent at the Depositary designated for such purposes in writing by the Warrant
Agent to the Depositary from time to time, (ii) an election to purchase (“Election to Purchase”) shares
of Common Stock pursuant to the exercise of a Warrant, properly completed and executed by the Registered Holder on the reverse of the
Definitive Warrant Certificate or, in the case of a Book-Entry Warrant Certificate, properly delivered by the Participant in accordance
with the Depositary’s procedures, and (iii) payment in full of the Warrant Price for each full share of Common Stock as to
which the Warrant is exercised and any and all applicable taxes due in connection with the exercise of the Warrant, the exchange of the
Warrant for the shares of Common Stock and the issuance of such shares of Common Stock, as follows:


 


(a) in
lawful money of the United States, in good certified check or good bank draft payable to the order of the Warrant Agent or by wire transfer
of immediately available funds;


 


(b) in
the event of a redemption pursuant to Section 6 hereof in which the Company’s board of directors (the “Board”)
has elected to require all holders of the Warrants to exercise such Warrants on a “cashless basis,” by surrendering the Warrants
for that number of shares of Common Stock equal to the quotient obtained by dividing (x) the product of the number of shares of Common
Stock underlying the Warrants, multiplied by the excess of the “Fair Market Value”, as defined in this subsection 3.3.1(b),
over the Warrant Price by (y) the Fair Market Value. Solely for purposes of this subsection 3.3.1(b) and Section 6.3,
the “Fair Market Value” shall mean the volume weighted average price of shares of the Common Stock for the ten (10) trading
days immediately following the date on which the notice of redemption is sent to the holders of the Warrants, pursuant to Section 6
hereof; or


 


(c) as
provided in Section 7.4 hereof.


 


The Warrant Agent shall forward
funds received for warrant exercises in a given month by the 5th Business Day of the following month by wire transfer to an account designated
by the Company.


 


3.3.2 Issuance
of Shares of Common Stock on Exercise. As soon as practicable after the exercise of any Warrant and the clearance of the funds in
payment of the Warrant Price (if payment is pursuant to subsection 3.3.1 (a)), the Company shall issue to the Registered Holder
of such Warrant a book-entry position or certificate, as applicable, for the number of full shares of Common Stock to which he, she or
it is entitled, registered in such name or names as may be directed by him, her or it, and if such Warrant shall not have been exercised
in full, a new book-entry position or countersigned Warrant, as applicable, for the number of shares of Common Stock as to which such
Warrant shall not have been exercised. If fewer than all the Warrants evidenced by a Book-Entry Warrant Certificate are exercised, a notation
shall be made to the records maintained by the Depositary, its nominee for each Book-Entry Warrant Certificate, or a Participant, as appropriate,
evidencing the balance of the Warrants remaining after such exercise. Notwithstanding the foregoing, the Company shall not be obligated
to deliver any shares of Common Stock pursuant to the exercise of a Warrant and shall have no obligation to settle such Warrant exercise
unless a registration statement under the Securities Act with respect to the shares of Common Stock underlying the Public Warrants is
then effective and a prospectus relating thereto is current, subject to the Company’s satisfying its obligations under Section 7.4.
No Warrant shall be exercisable and the Company shall not be obligated to issue shares of Common Stock upon exercise of a Warrant unless
the Common Stock issuable upon such Warrant exercise has been registered, qualified or deemed to be exempt from registration or qualification
under the securities laws of the state of residence of the Registered Holder of the Warrants. In the event that the conditions in the
two immediately preceding sentences are not satisfied with respect to a Warrant, the holder of such Warrant shall not be entitled to exercise
such Warrant and such Warrant may have no value and expire worthless, in which case the purchaser of a Unit containing such Public Warrants
shall have paid the full purchase price for the Unit solely for the shares of Common Stock underlying such Unit. In no event will the
Company be required to net cash settle the Warrant exercise. The Company may require holders of Public Warrants to settle the Warrant
on a “cashless basis” pursuant to Section 7.4. If, by reason of any exercise of Warrants on a “cashless
basis”, the holder of any Warrant would be entitled, upon the exercise of such Warrant, to receive a fractional interest in a share
of Common Stock, the Company shall round up to the nearest whole number, the number of shares of Common Stock to be issued to such holder.


 






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3.3.3 Valid
Issuance. All shares of Common Stock issued upon the proper exercise of a Warrant in conformity with this Agreement shall be validly
issued, fully paid and non-assessable.


 


3.3.4 Date
of Issuance. Each person in whose name any book-entry position or certificate, as applicable, for shares of Common Stock is issued
shall for all purposes be deemed to have become the holder of record of such shares of Common Stock on the date on which the Warrant,
or book-entry position representing such Warrant, was surrendered and payment of the Warrant Price was made, irrespective of the date
of delivery of such certificate in the case of a certificated Warrant, except that, if the date of such surrender and payment is a date
when the share transfer books of the Company or book-entry system of the Warrant Agent are closed, such person shall be deemed to have
become the holder of such shares of Common Stock at the close of business on the next succeeding date on which the share transfer books
or book-entry system are open.


 


3.3.5 Maximum
Percentage. A holder of a Warrant may notify the Company in writing in the event it elects to be subject to the provisions contained
in this subsection 3.3.5; however, no holder of a Warrant shall be subject to this subsection 3.3.5 unless he, she
or it makes such election. If the election is made by a holder, the Warrant Agent shall not effect the exercise of the holder’s
Warrant, and such holder shall not have the right to exercise such Warrant, to the extent that after giving effect to such exercise, such
person (together with such person’s affiliates), to the Warrant Agent’s actual knowledge, would beneficially own in excess
of 4.9% or 9.8% (or such other amount as a holder may specify) (the “Maximum Percentage”) of the shares of Common
Stock outstanding immediately after giving effect to such exercise. For purposes of the foregoing sentence, the aggregate number of shares
of Common Stock beneficially owned by such person and its affiliates shall include the number of shares of Common Stock issuable upon
exercise of the Warrant with respect to which the determination of such sentence is being made, but shall exclude shares of Common Stock
that would be issuable upon (x) exercise of the remaining, unexercised portion of the Warrant beneficially owned by such person and
its affiliates and (y) exercise or conversion of the unexercised or unconverted portion of any other securities of the Company beneficially
owned by such person and its affiliates (including, without limitation, any convertible notes or convertible preferred stock or warrants)
subject to a limitation on conversion or exercise analogous to the limitation contained herein. Except as set forth in the preceding sentence,
for purposes of this paragraph, beneficial ownership shall be calculated in accordance with Section 13(d) of the Securities Exchange Act
of 1934, as amended (the “Exchange Act”). For purposes of the Warrant, in determining the number of outstanding
shares of Common Stock, the holder may rely on the number of outstanding shares of Common Stock as reflected in (1) the Company’s
most recent Annual Report on Form 10-K, Quarterly Report on Form 10-Q, current report on Form 8-K or other public filing with the Commission
as the case may be, (2) a more recent public announcement by the Company or (3) any other notice by the Company or the Transfer
Agent setting forth the number of shares of Common Stock outstanding. For any reason at any time, upon the written request of the holder
of the Warrant, the Company shall, within two (2) Business Days, confirm orally and in writing to such holder the number of shares of
Common Stock then outstanding. In any case, the number of outstanding shares of Common Stock shall be determined after giving effect to
the conversion or exercise of equity securities of the Company by the holder and its affiliates since the date as of which such number
of outstanding shares of Common Stock was reported. By written notice to the Company, the holder of a Warrant may from time to time increase
or decrease the Maximum Percentage applicable to such holder to any other percentage specified in such notice; provided, however,
that any such increase shall not be effective until the sixty-first (61st) day after such notice is delivered to the Company.


 






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4. Adjustments.


 


4.1 Stock
Dividends.


 


4.1.1 Split-Ups.
If after the date hereof, and subject to the provisions of Section 4.6 hereof, the number of outstanding shares of Common Stock is increased
by a stock dividend payable in shares of Common Stock, or by a split up of shares of Common Stock, or other similar event, then, on the
effective date of such stock dividend, split up or similar event, the number of shares of Common Stock issuable on exercise of each Warrant
shall be increased in proportion to such increase in outstanding shares of Common Stock.


 


4.1.2 Extraordinary
Dividends. If the Company, at any time while the Warrants are outstanding and unexpired, shall pay a dividend or make a distribution
in cash, securities or other assets to the holders of the shares of Common Stock or other shares of the Company’s capital stock
into which the Warrants are convertible (an “Extraordinary Dividend”), then the Warrant Price shall be decreased,
effective immediately after the effective date of such Extraordinary Dividend, by the amount of cash and the fair market value (as determined
by the Company’s Board of Directors, in good faith) of any securities or other assets paid in respect of such Extraordinary Dividend
divided by all outstanding shares of the Company at such time (whether or not any shareholders waived their right to receive such dividend);
provided, however, that none of the following shall be deemed an Extraordinary Dividend for purposes of this provision: (a) any adjustment
described in subsection 4.1 above, (b) any cash dividends or cash distributions which, when combined on a per share basis with all other
cash dividends and cash distributions paid on the Common Stock during the 365-day period ending on the date of declaration of such dividend
or distribution does not exceed $0.50 per share (taking into account all of the outstanding shares of the Company at such time (whether
or not any shareholders waived their right to receive such dividend) and as adjusted to appropriately reflect any of the events referred
to in other subsections of this Section 4 and excluding cash dividends or cash distributions that resulted in an adjustment to the Warrant
Price or to the number of shares of Common Stock issuable on exercise of each Warrant) but only with respect to the amount of the aggregate
cash dividends or cash distributions equal to or less than $0.50, (c) any payment to satisfy the conversion rights of the holders of the
shares of Common Stock in connection with a proposed initial Business Combination or certain amendments to the Company’s Amended
and Restated Certificate of Incorporation (as described in the Registration Statement) or (d) any payment in connection with the Company’s
liquidation and the distribution of its assets upon its failure to consummate a Business Combination. Solely for purposes of illustration,
if the Company, at a time while the Warrants are outstanding and unexpired, pays a cash dividend of $0.35 and previously paid an aggregate
of $0.40 of cash dividends and cash distributions on the Common Stock during the 365-day period ending on the date of declaration of such
$0.35 dividend, then the Warrant Price will be decreased, effectively immediately after the effective date of such $0.35 dividend, by
$0.25 (the absolute value of the difference between $0.75 (the aggregate amount of all cash dividends and cash distributions paid or made
in such 365-day period, including such $0.35 dividend) and $0.50 (the greater of (x) $0.50 and (y) the aggregate amount of all cash dividends
and cash distributions paid or made in such 365-day period prior to such $0.35 dividend)). Furthermore, solely for the purposes of illustration,
if following the closing of the Company’s initial Business Combination, there were total shares outstanding of 100,000,000 and the
Company paid a $1.00 dividend to 17,500,000 of such shares (with the remaining 82,500,000 shares waiving their right to receive such dividend),
then no adjustment to the Warrant Price would occur as a $17.5 million dividend payment divided by 100,000,000 shares equals $0.175 per
share which is less than $0.50 per share.


 


4.2 Aggregation
of Shares. If after the date hereof, and subject to the provisions of Section 4.6 hereof, the number of outstanding shares
of Common Stock is decreased by a consolidation, combination, reverse stock split or reclassification of shares of Common Stock or other
similar event, then, on the effective date of such consolidation, combination, reverse stock split, reclassification or similar event,
the number of shares of Common Stock issuable on exercise of each Warrant shall be decreased in proportion to such decrease in outstanding
shares of Common Stock.


 






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4.3 Adjustments
in Warrant Price.


 


4.3.1 Whenever
the number of shares of Common Stock purchasable upon the exercise of the Warrants is adjusted, as provided in Sections 4.1 and 4.2 above,
the Warrant Price shall be adjusted (to the nearest cent) by multiplying such Warrant Price immediately prior to such adjustment by a
fraction (x) the numerator of which shall be the number of shares of Common Stock purchasable upon the exercise of the Warrants immediately
prior to such adjustment, and (y) the denominator of which shall be the number of shares of Common Stock so purchasable immediately thereafter.


 


4.3.2 If,
in connection with a Business Combination, the Company (a) issues additional shares of Common Stock or equity-linked securities at an
issue price or effective issue price of less than $9.20 per share (with such issue price or effective issue price as determined by the
Company’s Board of Directors, in good faith, and in the case of any such issuance to the Sponsor, the initial stockholders or their
affiliates, without taking into account any shares of the Company’s Class B common stock, par value $0.0001 per share (the “Class
B Common Stock”), issued prior to the Public Offering and held by the initial stockholders or their affiliates, as applicable,
prior to such issuance) (the “Newly Issued Price”), (b) the aggregate gross proceeds from such issuances represent
more than 60% of the total equity proceeds, and interest thereon, available for the funding of the Business Combination on the date of
the consummation of such Business Combination (net of redemptions), and (c) the Market Value (as defined below) is below $9.20 per share,
then the exercise price of the warrants will be adjusted (to the nearest cent) to be equal to 115% of the greater of (i) the Market Value
or (ii) Newly Issued Price, and the Redemption Trigger Price (as defined below) will be adjusted (to the nearest cent) to be equal to
180% of the greater of (i) the Market Value or (ii) the Newly Issued Price. Solely for purposes of this Section 4.3.2, the “Market
Value” shall mean the volume weighted average trading price of the Common Stock during the twenty (20) trading day period
starting on the trading day prior to the date of the consummation of the Business Combination.


 


4.4 Replacement
of Securities upon Reorganization, etc. In case of any reclassification or reorganization of the outstanding shares of Common Stock
(other than a change under subsections 4.1.1 or 4.1.2 or Section 4.2 hereof or that solely affects the
par value of such shares of Common Stock), or in the case of any merger or consolidation of the Company with or into another corporation
(other than a consolidation or merger in which the Company is the continuing corporation and that does not result in any reclassification
or reorganization of the outstanding Common Stock), or in the case of any sale or conveyance to another corporation or entity of the assets
or other property of the Company as an entirety or substantially as an entirety in connection with which the Company is dissolved, the
Warrant holders shall thereafter have the right to purchase and receive, upon the basis and upon the terms and conditions specified in
the Warrants and in lieu of the shares of Common Stock of the Company immediately theretofore purchasable and receivable upon the exercise
of the rights represented thereby, the kind and amount of shares of stock or other securities or property (including cash) receivable
upon such reclassification, reorganization, merger or consolidation, or upon a dissolution following any such sale or transfer, that the
Warrant holder would have received if such Warrant holder had exercised his, her or its Warrant(s) immediately prior to such event. If
any reclassification also results in a change in the Common Stock covered by subsections 4.1.1 or 4.1.2 or Section 4.2, then such adjustment
shall be made pursuant to Sections subsections 4.1.1 or 4.1.2, Section 4.2, subsection 4.3.1 and this Section 4.4. The provisions of this
Section 4.4 shall similarly apply to successive reclassifications, reorganizations, mergers or consolidations, sales or other transfers.
In no event will the Warrant Price be reduced to less than the par value per share issuable upon exercise of the Warrant.


 






    8


     


    

 


4.5 Notices
of Changes in Warrant. Upon every adjustment of the Warrant Price or the number of shares issuable upon exercise of a Warrant, the
Company shall give written notice thereof to the Warrant Agent, which notice shall state the Warrant Price resulting from such adjustment
and the increase or decrease, if any, in the number of shares purchasable at such price upon the exercise of a Warrant, setting forth
in reasonable detail the method of calculation and the facts upon which such calculation is based. Upon the occurrence of any event specified
in Sections 4.1, 4.2, 4.3 or 4.4, then, in any such event, the Company shall give written notice to each Warrant
holder, at the last address set forth for such holder in the Warrant Register, of the record date or the effective date of the event.
Failure to give such notice, or any defect therein, shall not affect the legality or validity of such event.


 


4.6 No
Fractional Shares. Notwithstanding any provision contained in this Agreement to the contrary, the Company shall not issue fractional
shares upon exercise of Warrants. If, by reason of any adjustment made pursuant to this Section 4, the holder of any Warrant would be
entitled, upon the exercise of such Warrant, to receive a fractional interest in a share, the Company shall, upon such exercise, round
up to the nearest whole number of shares of Common Stock to be issued to the Warrant holder.


 


4.7 Form
of Warrant. The form of Warrant need not be changed because of any adjustment pursuant to this Section 4, and Warrants issued after
such adjustment may state the same Warrant Price and the same number of shares as is stated in the Warrants initially issued pursuant
to this Agreement. However, the Company may at any time in its sole discretion make any change in the form of Warrant that the Company
may deem appropriate and that does not affect the substance thereof, and any Warrant thereafter issued or countersigned, whether in exchange
or substitution for an outstanding Warrant or otherwise, may be in the form as so changed.


 


4.8 Other
Events. In case any event shall occur affecting the Company as to which none of the provisions of preceding subsections of this Section
4 are strictly applicable, but which would require an adjustment to the terms of the Warrants in order to (i) avoid an adverse impact
on the Warrants and (ii) effectuate the intent and purpose of this Section 4, then, in each such case, the Company shall appoint a firm
of independent public accountants, investment banking or other appraisal firm of recognized national standing, which shall give its opinion
as to whether or not any adjustment to the rights represented by the Warrants is necessary to effectuate the intent and purpose of this
Section 4 and, if they determine that an adjustment is necessary, the terms of such adjustment. The Company shall adjust the terms of
the Warrants in a manner that is consistent with any adjustment recommended in such opinion.


 


4.9 No
Adjustment. For the avoidance of doubt, no adjustment shall be made to the terms of the Warrants solely as a result of an adjustment
to the conversion ratio of the Class B Common Stock into shares of Common Stock or the conversion of the shares of Class B Common Stock
into shares of Common Stock, in each case, pursuant to the Company’s Amended and Restated Certificate of Incorporation, as further
amended from time to time.


 






    9


     


    

 


5. Transfer
and Exchange of Warrants.


 


5.1 Registration
of Transfer. The Warrant Agent shall register the transfer, from time to time, of any outstanding Warrant upon the Warrant Register,
upon surrender of such Warrant for transfer, in the case of a certificated Warrant, properly endorsed with signatures properly guaranteed
and accompanied by appropriate instructions for transfer. Upon any such transfer, a new Warrant representing an equal aggregate number
of Warrants shall be issued and the old Warrant shall be cancelled by the Warrant Agent. In the case of certificated Warrants, the Warrants
so cancelled shall be delivered by the Warrant Agent to the Company from time to time upon request.


 


5.2 Procedure
for Surrender of Warrants. Warrants may be surrendered to the Warrant Agent, together with a written request for exchange or transfer,
and thereupon the Warrant Agent shall issue in exchange therefor one or more new Warrants as requested by the Registered Holder of the
Warrants so surrendered, representing an equal aggregate number of Warrants; provided, however, that except as otherwise
provided herein or in any Book-Entry Warrant Certificate or Definitive Warrant Certificate, each Book-Entry Warrant Certificate and Definitive
Warrant Certificate may be transferred only in whole and only to the Depositary, to another nominee of the Depositary, to a successor
depository, or to a nominee of a successor depository; provided further, however, that in the event that a Warrant
surrendered for transfer bears a restrictive legend (as in the case of the Private Placement Warrants and the Working Capital Warrants),
the Warrant Agent shall not cancel such Warrant and issue new Warrants in exchange thereof until the Warrant Agent has received an opinion
of counsel for the Company stating that such transfer may be made and indicating whether the new Warrants must also bear a restrictive
legend.


 


5.3 Fractional
Warrants. The Warrant Agent shall not be required to effect any registration of transfer or exchange which shall result in the issuance
of a warrant certificate or book-entry position for a fraction of a warrant, except as part of the Units.


 


5.4 Service
Charges. No service charge shall be made for any exchange or registration of transfer of Warrants.


 


5.5 Warrant
Execution and Countersignature. The Warrant Agent is hereby authorized to countersign and to deliver, in accordance with the terms
of this Agreement, the Warrants required to be issued pursuant to the provisions of this Section 5, and the Company, whenever
required by the Warrant Agent, shall supply the Warrant Agent with Warrants duly executed on behalf of the Company for such purpose.


 


5.6 Transfer
of Warrants. Prior to the Detachment Date, the Public Warrants may be transferred or exchanged only together with the Unit in which
such Warrant is included, and only for the purpose of effecting, or in conjunction with, a transfer or exchange of such Unit. Furthermore,
each transfer of a Unit on the register relating to such Units shall operate also to transfer the Warrants included in such Unit. Notwithstanding
the foregoing, the provisions of this Section 5.6 shall have no effect on any transfer of Warrants on and after the Detachment
Date.


 






    10


     


    

 


6. Redemption.


 


6.1 Redemption
of Warrants for Cash. Not less than all of the outstanding Warrants may be redeemed, at the option of the Company, at any time while
they are exercisable and prior to their expiration, at the office of the Warrant Agent, upon notice to the Registered Holders of the Warrants,
as described in Section 6.2 below, at the price of $0.01 per Warrant (the “Redemption Price”); provided
that the closing price of the Common Stock reported has been at least $18.00 per share (subject to adjustment in compliance with Section 4
hereof) (the “Redemption Trigger Price”), on each of twenty (20) trading days within the thirty (30) trading-day
period ending on the third Business Day prior to the date on which notice of the redemption is given; provided further that there
is an effective registration statement covering the shares of Common Stock issuable upon exercise of the Warrants, and a current prospectus
relating thereto, available throughout the 30-day Redemption Period (as defined in Section 6.2 below) or the Company has elected
to require the exercise of the Warrants on a “cashless basis” pursuant to subsection 3.3.1 and such cashless exercise
is exempt from registration under the Securities Act.


 


6.2 Date
Fixed for, and Notice of, Redemption. In the event the Company shall elect to redeem all of the Warrants that are subject to redemption,
the Company shall fix a date for the redemption (the “Redemption Date”). Notice of redemption shall be mailed
by first class mail, postage prepaid, by the Company not less than thirty (30) days prior to the Redemption Date (such period, the “Redemption
Period”) to the registered holders of the Warrants to be redeemed at their last addresses as they shall appear on the registration
books. Any notice mailed in the manner herein provided shall be conclusively presumed to have been duly given whether or not the registered
holder received such notice


 


6.3 Exercise
After Notice of Redemption. The Warrants may be exercised, for cash (or on a “cashless basis” in accordance with Section
3 of this Agreement) at any time after notice of redemption shall have been given by the Company pursuant to Section 6.2 hereof and prior
to the Redemption Date. In the event the Company determines to require all holders of Warrants to exercise their Warrants on a “cashless
basis” pursuant to Section 3.3.1(b), the notice of redemption will contain the information necessary to calculate the number of
shares of Common Stock to be received upon exercise of the Warrants, including the “Fair Market Value” in such case. On and
after the Redemption Date, the record holder of the Warrants shall have no further rights except to receive, upon surrender of the Warrants,
the Redemption Price.


 


7. Other
Provisions Relating to Rights of Holders of Warrants.


 


7.1 No
Rights as Stockholder. A Warrant does not entitle the Registered Holder thereof to any of the rights of a stockholder of the Company,
including, without limitation, the right to receive dividends, or other distributions, exercise any preemptive rights to vote or to consent
or to receive notice as stockholders in respect of the meetings of stockholders or the election of directors of the Company or any other
matter.


 


7.2 Lost,
Stolen, Mutilated, or Destroyed Warrants. If any Warrant is lost, stolen, mutilated, or destroyed, the Company and the Warrant Agent
may on such terms as to indemnity or otherwise as they may in their discretion impose (which shall, in the case of a mutilated Warrant,
include the surrender thereof), issue a new Warrant of like denomination, tenor, and date as the Warrant so lost, stolen, mutilated, or
destroyed. Any such new Warrant shall constitute a substitute contractual obligation of the Company, whether or not the allegedly lost,
stolen, mutilated, or destroyed Warrant shall be at any time enforceable by anyone.


 






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7.3 Reservation
of Common Stock. The Company shall at all times reserve and keep available a number of its authorized but unissued shares of Common
Stock that shall be sufficient to permit the exercise in full of all outstanding Warrants issued pursuant to this Agreement.


 


7.4 Registration
of Common Stock; Cashless Exercise at Company’s Option. The Company agrees that as soon as practicable after the closing of
its initial Business Combination, it shall use its best efforts to file with the SEC a registration statement for the registration, under
the Act, of the shares of Common Stock issuable upon exercise of the Warrants, and it shall use its best efforts to take such action as
is necessary to register or qualify for sale, in those states in which the Warrants were initially offered by the Company and in those
states where holders of Warrants then reside, the shares of Common Stock issuable upon exercise of the Warrants, to the extent an exemption
is not available. The Company will use its best efforts to cause the same to become effective and to maintain the effectiveness of such
registration statement until the expiration of the Warrants in accordance with the provisions of this Agreement. If any such registration
statement has not been declared effective by the 60th Business Day following the closing of the Business Combination, holders of the Warrants
shall have the right, during the period beginning on the 61st Business Day after the closing of the Business Combination and ending upon
such registration statement being declared effective by the SEC, and during any other period when the Company shall fail to have maintained
an effective registration statement covering the shares of Common Stock issuable upon exercise of the Warrants, to exercise such Warrants
on a “cashless basis” as determined in accordance with Section 3.3.1(d). The Company shall provide the Warrant Agent with
an opinion of counsel for the Company (which shall be an outside law firm with securities law experience) stating that (i) the exercise
of the Warrants on a cashless basis in accordance with this Section 7.4 is not required to be registered under the Act and (ii) the shares
of Common Stock issued upon such exercise will be freely tradable under U.S. federal securities laws by anyone who is not an affiliate
(as such term is defined in Rule 144 under the Act) of the Company and, accordingly, will not be required to bear a restrictive legend.
For the avoidance of any doubt, unless and until all of the Warrants have been exercised on a cashless basis, the Company shall continue
to be obligated to comply with its registration obligations under the first three sentences of this Section 7.4.


 


8. Concerning
the Warrant Agent and Other Matters.


 


8.1 Payment
of Taxes. The Company shall from time to time promptly pay all taxes and charges that may be imposed upon the Company or the Warrant
Agent in respect of the issuance or delivery of shares of Common Stock upon the exercise of the Warrants, but the Company shall not be
obligated to pay any transfer taxes in respect of the Warrants or such shares of Common Stock.


 


8.2 Resignation,
Consolidation, or Merger of Warrant Agent.


 


8.2.1 Appointment
of Successor Warrant Agent. The Warrant Agent, or any successor to it hereafter appointed, may resign its duties and be discharged
from all further duties and liabilities hereunder after giving sixty (60) days’ notice in writing to the Company. If the office
of the Warrant Agent becomes vacant by resignation or incapacity to act or otherwise, the Company shall appoint in writing a successor
Warrant Agent in place of the Warrant Agent. If the Company shall fail to make such appointment within a period of thirty (30) days after
it has been notified in writing of such resignation or incapacity by the Warrant Agent or by the holder of a Warrant (who shall, with
such notice, submit his, her or its Warrant for inspection by the Company), then the holder of any Warrant may apply to the Supreme Court
of the State of New York for the County of New York for the appointment of a successor Warrant Agent at the Company’s cost. Any
successor Warrant Agent, whether appointed by the Company or by such court, shall be a corporation organized and existing under the laws
of the State of New York, in good standing and having its principal office in the Borough of Manhattan, City and State of New York, and
authorized under such laws to exercise corporate trust powers and subject to supervision or examination by federal or state authority.
After appointment, any successor Warrant Agent shall be vested with all the authority, powers, rights, immunities, duties, and obligations
of its predecessor Warrant Agent with like effect as if originally named as Warrant Agent hereunder, without any further act or deed;
but if for any reason it becomes necessary or appropriate, the predecessor Warrant Agent shall execute and deliver, at the expense of
the Company, an instrument transferring to such successor Warrant Agent all the authority, powers, and rights of such predecessor Warrant
Agent hereunder; and upon request of any successor Warrant Agent the Company shall make, execute, acknowledge, and deliver any and all
instruments in writing for more fully and effectually vesting in and confirming to such successor Warrant Agent all such authority, powers,
rights, immunities, duties, and obligations.


 






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8.2.2 Notice
of Successor Warrant Agent. In the event a successor Warrant Agent shall be appointed, the Company shall give notice thereof to the
predecessor Warrant Agent and the Transfer Agent for the Common Stock not later than the effective date of any such appointment.


 


8.2.3 Merger
or Consolidation of Warrant Agent. Any corporation into which the Warrant Agent may be merged or with which it may be consolidated
or any corporation resulting from any merger or consolidation to which the Warrant Agent shall be a party shall be the successor Warrant
Agent under this Agreement without any further act.


 


8.3 Fees
and Expenses of Warrant Agent.


 


8.3.1 Remuneration.
The Company agrees to pay the Warrant Agent reasonable remuneration for its services as such Warrant Agent hereunder and shall, pursuant
to its obligations under this Agreement, reimburse the Warrant Agent upon demand for all expenditures that the Warrant Agent may reasonably
incur in the execution of its duties hereunder.


 


8.3.2 Further
Assurances. The Company agrees to perform, execute, acknowledge, and deliver or cause to be performed, executed, acknowledged, and
delivered all such further and other acts, instruments, and assurances as may reasonably be required by the Warrant Agent for the carrying
out or performing of the provisions of this Agreement.


 


8.4 Liability
of Warrant Agent.


 


8.4.1 Reliance
on Company Statement. Whenever in the performance of its duties under this Agreement, the Warrant Agent shall deem it necessary or
desirable that any fact or matter be proved or established by the Company prior to taking or suffering any action hereunder, such fact
or matter (unless other evidence in respect thereof be herein specifically prescribed) may be deemed to be conclusively proved and established
by a statement signed by the Chief Executive Officer, Chief Financial Officer, President, Executive Vice President, Vice President, Secretary
or Chairman of the Board of the Company and delivered to the Warrant Agent. The Warrant Agent may rely upon such statement for any action
taken or suffered in good faith by it pursuant to the provisions of this Agreement.


 


8.4.2 Indemnity.
The Warrant Agent shall be liable hereunder only for its own gross negligence, willful misconduct or bad faith. The Company agrees to
indemnify the Warrant Agent and save it harmless against any and all liabilities, including judgments, costs and reasonable counsel fees,
for anything done or omitted by the Warrant Agent in the execution of this Agreement, except as a result of the Warrant Agent’s
gross negligence, willful misconduct or bad faith.


 


8.4.3 Exclusions.
The Warrant Agent shall have no responsibility with respect to the validity of this Agreement or with respect to the validity or execution
of any Warrant (except its countersignature thereof). The Warrant Agent shall not be responsible for any breach by the Company of any
covenant or condition contained in this Agreement or in any Warrant. The Warrant Agent shall not be responsible to make any adjustments
required under the provisions of Section 4 hereof or responsible for the manner, method, or amount of any such adjustment
or the ascertaining of the existence of facts that would require any such adjustment; nor shall it by any act hereunder be deemed to make
any representation or warranty as to the authorization or reservation of any shares of Common Stock to be issued pursuant to this Agreement
or any Warrant or as to whether any shares of Common Stock shall, when issued, be valid and fully paid and non-assessable.


 


8.5 Acceptance
of Agency. The Warrant Agent hereby accepts the agency established by this Agreement and agrees to perform the same upon the terms
and conditions herein set forth and among other things, shall account promptly to the Company with respect to Warrants exercised and concurrently
account for, and pay to the Company, all monies received by the Warrant Agent for the purchase of shares of Common Stock through the exercise
of the Warrants.


 






    13


     


    

 


8.6 Waiver.
The Warrant Agent has no right of set-off or any other right, title, interest or claim of any kind (“Claim”)
in, or to any distribution of, the Trust Account (as defined in that certain Investment Management Trust Agreement, dated as of the date
hereof, by and between the Company and the Warrant Agent as trustee thereunder) and hereby agrees not to seek recourse, reimbursement,
payment or satisfaction for any Claim against the Trust Account for any reason whatsoever. The Warrant Agent hereby waives any and all
Claims against the Trust Account and any and all rights to seek access to the Trust Account.


 


9. Miscellaneous
Provisions.


 


9.1 Successors.
All the covenants and provisions of this Agreement by or for the benefit of the Company or the Warrant Agent shall bind and inure to the
benefit of their respective successors and assigns.


 


9.2 Notices.
Any notice, statement or demand authorized by this Agreement to be given or made by the Warrant Agent or by the holder of any Warrant
to or on the Company shall be sufficiently given when so delivered if by hand or overnight delivery or if sent by certified mail or private
courier service within five (5) days after deposit of such notice, postage prepaid, addressed (until another address is filed in writing
by the Company with the Warrant Agent), as follows:


 


	
     

    
	Alpha Healthcare Acquisition Corp. III
	 	1177 Avenue of the Americas, 5th Floor
	 	New York, New York 10036
	 	Attention: Chief Executive Officer



 


Any notice, statement or demand authorized by
this Agreement to be given or made by the holder of any Warrant or by the Company to or on the Warrant Agent shall be sufficiently given
when so delivered if by hand or overnight delivery or if sent by certified mail or private courier service within five (5) days after
deposit of such notice, postage prepaid, addressed (until another address is filed in writing by the Warrant Agent with the Company),
as follows:


 


	 	
    Continental Stock Transfer & Trust Company

	 	1 State Street, 30th Floor
	 	New York, NY 10004
	 	Attention: Compliance Department



 


in each case, with copies to:


 


	 	
    Goodwin Procter LLP

	 	620 Eighth Avenue
	 	New York, New York 10018
	 	Attn: Thomas Levato, Esq.
	 	Email: tlevato@goodwinlaw.com



 






    14


     


    

 


9.3 Applicable
Law. The validity, interpretation, and performance of this Agreement and of the Warrants shall be governed in all respects by the
laws of State of New York. The Company hereby agrees that any action, proceeding or claim against it arising out of or relating in any
way to this Agreement shall be brought and enforced in the courts of the State of New York or the United States District Courts located
in the State of New York, and irrevocably submits to such jurisdiction, which jurisdiction shall be exclusive. The Company hereby waives
any objection to such exclusive jurisdiction and that such courts represent an inconvenient forum.


 


9.4 Persons
Having Rights under this Agreement. Nothing in this Agreement shall be construed to confer upon, or give to, any person or corporation
other than the parties hereto and the Registered Holders of the Warrants any right, remedy, or claim under or by reason of this Agreement
or of any covenant, condition, stipulation, promise, or agreement hereof. All covenants, conditions, stipulations, promises, and agreements
contained in this Agreement shall be for the sole and exclusive benefit of the parties hereto and their successors and assigns and of
the Registered Holders of the Warrants.


 


9.5 Examination
of the Warrant Agreement. A copy of this Agreement shall be available at all reasonable times at the office of the Warrant Agent in
the Borough of Manhattan, City and State of New York, for inspection by the Registered Holder of any Warrant. The Warrant Agent may require
any such holder to submit such holder’s Warrant for inspection by the Warrant Agent.


 


9.6 Counterparts.
This Agreement may be executed in any number of original or facsimile counterparts and each of such counterparts shall for all purposes
be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument.


 


9.7 Effect
of Headings. The section headings herein are for convenience only and are not part of this Agreement and shall not affect the interpretation
thereof.


 


9.8 Amendments.
This Agreement may be amended by the parties hereto without the consent of any registered holder for the purpose of (i) curing any ambiguity
or to correct any mistake, including to conform the provisions hereof to the description of the terms of the Warrants and this Agreement
set forth in the Prospectus, or curing, correcting or supplementing any defective provision contained herein, or (ii) adding or changing
any other provisions with respect to matters or questions arising under this Agreement as the parties may deem necessary or desirable
and that the parties deem shall not adversely affect the interest of the registered holders. All other modifications or amendments, including
any amendment to increase the Warrant Price or shorten the Exercise Period, shall require the written consent or vote of the registered
holders of at least 50% of the then outstanding Public Warrants. Notwithstanding the foregoing, the Company may lower the Warrant Price
or extend the duration of the Exercise Period pursuant to Sections 3.1 and 3.2, respectively, without the consent of the
Registered Holders.


 


9.9 Severability.
This Agreement shall be deemed severable, and the invalidity or unenforceability of any term or provision hereof shall not affect the
validity or enforceability of this Agreement or of any other term or provision hereof. Furthermore, in lieu of any such invalid or unenforceable
term or provision, the parties hereto intend that there shall be added as a part of this Agreement a provision as similar in terms to
such invalid or unenforceable provision as may be possible and be valid and enforceable.


 


[Signature Page Follows]


 




    15


     


    

 


IN WITNESS WHEREOF, the parties
hereto have caused this Agreement to be duly executed as of the date first above written.


 


	 	CONTINENTAL STOCK TRANSFER & TRUST COMPANY, as Warrant Agent
	 	 	 	 
	 	By:	/s/ Henry Farrell
	 	 	Name:	Henry Farrell
	 	 	Title:	Vice President
	 	 	 	 
	 	ALPHA HEALTHCARE ACQUISITION CORP. III
	 	 	 	 
	 	By:	/s/ Patrick A. Strugeon
	 	 	Name:	Patrick A. Sturgeon
	 	 	Title:	Chief Financial Officer


 


[Signature Page to Warrant Agreement]


 




     


     


    

 


EXHIBIT A


 


FORM OF WARRANT CERTIFICATE


 


[FACE]


 


Number


 


Warrants


 


THIS WARRANT SHALL BE VOID IF NOT EXERCISED
PRIOR TO THE EXPIRATION OF THE EXERCISE PERIOD PROVIDED FOR IN THE WARRANT AGREEMENT DESCRIBED BELOW


 


ALPHA HEALTHCARE ACQUISITION CORP. III


Incorporated Under the Laws of the State of
Delaware


 


CUSIP 02073F112


 


Warrant Certificate


 


This Warrant Certificate
certifies that     , or registered assigns, is the registered holder
of warrant(s) evidenced hereby (the “Warrants” and each, a “Warrant”) to purchase
shares of Class A common stock, $0.0001 par value per share (“Class A Common Stock”), of Alpha Healthcare Acquisition
Corp. III, a Delaware corporation (the “Company”). Each whole Warrant entitles the holder, upon exercise during
the period set forth in the Warrant Agreement referred to below, to receive from the Company that number of fully paid and non-assessable
shares of Class A Common Stock as set forth below, at the exercise price (the “Warrant Price”) as determined
pursuant to the Warrant Agreement, payable in lawful money (or through “cashless exercise” as provided for in
the Warrant Agreement) of the United States of America upon surrender of this Warrant Certificate and payment of the Warrant Price at
the office or agency of the Warrant Agent referred to below, subject to the conditions set forth herein and in the Warrant Agreement.
Defined terms used in this Warrant Certificate but not defined herein shall have the meanings given to them in the Warrant Agreement.


 


Each whole Warrant is initially
exercisable for one fully paid and non-assessable share of Class A Common Stock. No fractional shares will be issued upon exercise of
any Warrant. If, upon the exercise of Warrants, a holder would be entitled to receive a fractional interest in a share of Class A Common
Stock, the Company will, upon exercise, round down to the nearest whole number the number of shares of Class A Common Stock to be issued
to the Warrant holder. The number of shares of Class A Common Stock issuable upon exercise of the Warrants is subject to adjustment upon
the occurrence of certain events set forth in the Warrant Agreement.


 


The initial Warrant Price
per share of Class A Common Stock for any Warrant is equal to $11.50 per share. The Warrant Price is subject to adjustment upon the occurrence
of certain events set forth in the Warrant Agreement.


 


Subject to the conditions
set forth in the Warrant Agreement, the Warrants may be exercised only during the Exercise Period and to the extent not exercised by the
end of such Exercise Period, such Warrants shall become void.


 




     


     


    

 


Reference is hereby made to
the further provisions of this Warrant Certificate set forth on the reverse hereof and such further provisions shall for all purposes
have the same effect as though fully set forth at this place.


 


This Warrant Certificate
shall not be valid unless countersigned by the Warrant Agent, as such term is used in the Warrant Agreement.


 


	 	ALPHA HEALTHCARE ACQUISITION CORP. III
	 	 
	 	By:	                      
	 	Name:	 
	 	Title:	 
	 	 
	 	CONTINENTAL STOCK TRANSFER & TRUST COMPANY,
	 	AS WARRANT AGENT
	 	 
	 	By:	 
	 	Name:	 
	 	Title:	 


 




     


     


    

 


[Form of Warrant Certificate]


 


[Reverse]


 


The Warrants evidenced by this Warrant Certificate
are part of a duly authorized issue of Warrants entitling the holder on exercise to receive shares of Class A Common Stock and are issued
or to be issued pursuant to a Warrant Agreement dated as of July 26, 2021 (the
“Warrant Agreement”), duly executed and delivered by the Company to Continental Stock Transfer & Trust Company,
a New York corporation, as warrant agent (the “Warrant Agent”), which Warrant Agreement is hereby incorporated
by reference in and made a part of this instrument and is hereby referred to for a description of the rights, limitation of rights, obligations,
duties and immunities thereunder of the Warrant Agent, the Company and the holders (the words “holders” or “holder”
meaning the Registered Holders or Registered Holder, respectively) of the Warrants. A copy of the Warrant Agreement may be obtained by
the holder hereof upon written request to the Company. Defined terms used in this Warrant Certificate but not defined herein shall have
the meanings given to them in the Warrant Agreement.


 


Warrants may be exercised at any time during the
Exercise Period set forth in the Warrant Agreement. The holder of Warrants evidenced by this Warrant Certificate may exercise them by
surrendering this Warrant Certificate, with the form of election to purchase set forth hereon properly completed and executed, together
with payment of the Warrant Price as specified in the Warrant Agreement (or through “cashless exercise” as provided for in
the Warrant Agreement) at the principal corporate trust office of the Warrant Agent. In the event that upon any exercise of Warrants evidenced
hereby the number of Warrants exercised shall be less than the total number of Warrants evidenced hereby, there shall be issued to the
holder hereof or his, her or its assignee, a new Warrant Certificate evidencing the number of Warrants not exercised.


 


Notwithstanding anything else in this Warrant
Certificate or the Warrant Agreement, no Warrant may be exercised unless at the time of exercise (i) a registration statement covering
the shares of Class A Common Stock to be issued upon exercise is effective under the Securities Act and (ii) a prospectus thereunder relating
to the shares of Class A Common Stock is current, except through “cashless exercise” as provided for in the Warrant Agreement.


 


The Warrant Agreement provides that upon the occurrence
of certain events the number of shares of Class A Common Stock issuable upon exercise of the Warrants set forth on the face hereof may,
subject to certain conditions, be adjusted. If, upon exercise of a Warrant, the holder thereof would be entitled to receive a fractional
interest in a share of Class A Common Stock, the Company shall, upon exercise, round down to the nearest whole number of shares of Class
A Common Stock to be issued to the holder of the Warrant.


 


Warrant Certificates, when surrendered at the
principal corporate trust office of the Warrant Agent by the Registered Holder thereof in person or by legal representative or attorney
duly authorized in writing, may be exchanged, in the manner and subject to the limitations provided in the Warrant Agreement, but without
payment of any service charge, for another Warrant Certificate or Warrant Certificates of like tenor evidencing in the aggregate a like
number of Warrants.


 


Upon due presentation for registration of transfer
of this Warrant Certificate at the office of the Warrant Agent a new Warrant Certificate or Warrant Certificates of like tenor and evidencing
in the aggregate a like number of Warrants shall be issued to the transferee(s) in exchange for this Warrant Certificate, subject to the
limitations provided in the Warrant Agreement, without charge except for any tax or other governmental charge imposed in connection therewith.


 


The Company and the Warrant Agent may deem and
treat the Registered Holder(s) hereof as the absolute owner(s) of this Warrant Certificate (notwithstanding any notation of ownership
or other writing hereon made by anyone), for the purpose of any exercise hereof, of any distribution to the holder(s) hereof, and for
all other purposes, and neither the Company nor the Warrant Agent shall be affected by any notice to the contrary. Neither the Warrants
nor this Warrant Certificate entitles any holder hereof to any rights of a stockholder of the Company.


 




     


     


    

 


Election to Purchase


 


(To Be Executed Upon Exercise of Warrant)


 


The undersigned hereby irrevocably elects to exercise
the right, represented by this Warrant Certificate, to receive shares of Class A Common Stock and herewith tenders payment for such shares
of Class A Common Stock to the order of Alpha Healthcare Acquisition Corp. III (the “Company”) in the amount
of $ in accordance with the terms hereof. The undersigned requests that a certificate for such shares of Class A Common Stock be registered
in the name of , whose address is and that such shares of Class A Common Stock be delivered to whose address is . If said number of shares
of Class A Common Stock is less than all of the shares of Class A Common Stock purchasable hereunder, the undersigned requests that a
new Warrant Certificate representing the remaining balance of such shares of Class A Common Stock be registered in the name of , whose
address is and that such Warrant Certificate be delivered to , whose address is .


 


In the event that the Warrant has been called
for redemption by the Company pursuant to Section 6.1 or 6.2 of the Warrant Agreement and the Company
has required cashless exercise pursuant to Section 6.4 of the Warrant Agreement, the number of shares of Class A Common
Stock that this Warrant is exercisable for shall be determined in accordance with subsection 3.3.1(b) and Section
6.4 of the Warrant Agreement.


 


In the event that the Warrant is a Private Placement
Warrant or a Working Capital Warrant that is to be exercised on a “cashless” basis pursuant to subsection 3.3.1(c) of
the Warrant Agreement, the number of shares of Class A Common Stock that this Warrant is exercisable for shall be determined in accordance
with subsection 3.3.1(c) of the Warrant Agreement.


 


In the event that the Warrant is to be exercised
on a “cashless” basis pursuant to Section 7.4 of the Warrant Agreement, the number of shares of Class A Common
Stock that this Warrant is exercisable for shall be determined in accordance with Section 7.4 of the Warrant Agreement.


 


In the event that the Warrant may be exercised,
to the extent allowed by the Warrant Agreement, through cashless exercise (i) the number of shares of Class A Common Stock that this Warrant
is exercisable for would be determined in accordance with the relevant section of the Warrant Agreement which allows for such cashless
exercise and (ii) the holder hereof shall complete the following: The undersigned hereby irrevocably elects to exercise the right, represented
by this Warrant Certificate, through the cashless exercise provisions of the Warrant Agreement, to receive shares of Class A Common Stock.
If said number of shares of Class A Common Stock is less than all of the shares of Class A Common Stock purchasable hereunder (after giving
effect to the cashless exercise), the undersigned requests that a new Warrant Certificate representing the remaining balance of such shares
of Class A Common Stock be registered in the name of , whose address is and that such Warrant Certificate be delivered to , whose address
is.


 


[Signature Page Follows]


 




     


     


    

 


	Date: [_____], 20[__]	 
	 	 
	 	 
	 	(Signature)
	 	 
	 	(Address)
	 	 
	 	(Tax Identification Number)


 


Signature Guaranteed:


 


	 	 
	 	 
	THE SIGNATURE(S) SHOULD BE GUARANTEED BY AN ELIGIBLE GUARANTOR INSTITUTION (BANKS, STOCKBROKERS, SAVINGS AND LOAN ASSOCIATIONS AND CREDIT UNIONS WITH MEMBERSHIP IN AN APPROVED SIGNATURE GUARANTEE MEDALLION PROGRAM, PURSUANT TO S.E.C. RULE 17Ad-15 UNDER THE SECURITIES EXCHANGE ACT OF 1934, AS AMENDED (OR ANY SUCCESSOR RULE)).	 


 




     


     


    

 


EXHIBIT B


 


LEGEND


 


Class A Common Stock Legend:


 


“THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED
UNDER THE UNITED STATES SECURITIES ACT OF 1933, AS AMENDED, OR ANY STATE SECURITIES LAWS, AND NEITHER THE SECURITIES NOR ANY
INTEREST THEREIN MAY BE OFFERED, SOLD, TRANSFERRED, PLEDGED OR OTHERWISE DISPOSED OF EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION
STATEMENT UNDER SUCH ACT OR SUCH LAWS OR AN EXEMPTION FROM REGISTRATION UNDER SUCH ACT AND SUCH LAWS WHICH, IN THE OPINION OF
COUNSEL, IS AVAILABLE.


 


THE SECURITIES REPRESENTED BY THIS CERTIFICATE ARE SUBJECT TO
LOCKUP PROVISIONS AND MAY NOT BE OFFERED, SOLD, TRANSFERRED, PLEDGED OR OTHERWISE DISPOSED OF DURING THE TERM OF THE
LOCKUP.”


 


Warrant Legend:


 


“THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT
BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY STATE SECURITIES LAWS, AND MAY NOT BE OFFERED, SOLD,
TRANSFERRED OR OTHERWISE DISPOSED OF UNLESS REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, AND ANY APPLICABLE STATE
SECURITIES LAWS OR AN EXEMPTION FROM REGISTRATION IS AVAILABLE. IN ADDITION, SUBJECT TO ANY ADDITIONAL LIMITATIONS ON TRANSFER
DESCRIBED IN THE LETTER AGREEMENT BY AND AMONG ALPHA HEALTHCARE ACQUISITION CORP. III (THE “COMPANY”), AHAC SPONSOR III
LLC AND THE OTHER PARTIES THERETO, THE SECURITIES REPRESENTED BY THIS CERTIFICATE MAY NOT BE SOLD OR TRANSFERRED PRIOR TO THE DATE
THAT IS THIRTY (30) DAYS AFTER THE DATE UPON WHICH THE COMPANY COMPLETES ITS INITIAL BUSINESS COMBINATION (AS DEFINED IN THE
RECITALS OF THE WARRANT AGREEMENT REFERRED TO HEREIN) EXCEPT TO A PERMITTED TRANSFEREE (AS DEFINED IN SECTION 2 OF THE WARRANT
AGREEMENT) WHO AGREES IN WRITING WITH THE COMPANY TO BE SUBJECT TO SUCH TRANSFER


PROVISIONS.


 


THE SECURITIES REPRESENTED BY THIS CERTIFICATE AND THE SHARES OF
CLASS A COMMON STOCK OF THE COMPANY ISSUED UPON EXERCISE OF SUCH SECURITIES SHALL BE ENTITLED TO REGISTRATION RIGHTS UNDER A
REGISTRATION RIGHTS AGREEMENT TO BE EXECUTED BY THE COMPANY.”