Exhibit 4.5


 





FORM OF PRIVATE PLACEMENT WARRANT
AGREEMENT


between

APOLLO STRATEGIC GROWTH CAPITAL III

and

CONTINENTAL STOCK TRANSFER & TRUST COMPANY


 


Dated as of [        ], 2022


 


THIS WARRANT AGREEMENT (this “Agreement”),
dated as of [     ], 2022, is by and between Apollo Strategic Growth Capital III, a Cayman Islands exempted company and incorporated with
limited liability (the “Company”), and Continental Stock Transfer & Trust Company, a New York corporation, as warrant
agent (the “Warrant Agent,” also referred to herein as the “Transfer Agent”).


 


WHEREAS, on [     ], 2022, the Company entered into
that certain Private Placement Warrants Purchase Agreement with APSG Sponsor III, L.P., a Cayman Islands exempted limited partnership
(the “Sponsor”), pursuant to which the Sponsor will purchase an aggregate of 6,107,500 warrants (or up to 6,807,500
warrants if the over-allotment option is exercised in full) simultaneously with the closing of the Offering (and the closing of the over-allotment
option, if applicable) bearing the legend set forth in Exhibit A hereto (the “Private Placement Warrants”) at
a purchase price of $1.50 per Private Placement Warrant;


 


WHEREAS, in order to finance the Company’s
transaction costs in connection with an intended initial Business Combination (as defined below), the Sponsor or affiliates of the Sponsor
or certain of the Company’s officers and directors may, but are not obligated to, loan the Company funds as the Company may require,
of which up to $2,000,000 of such loans may be convertible into up to an additional 1,333,333 Private Placement Warrants (the “Working
Capital Warrants” and, together with the Private Placement Warrants, the “Warrants”) at a price of $1.50
per warrant;


 


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 Class
A Ordinary Share, par value $0.0001 per share (“Ordinary Shares”), and one-third of one public warrant (the “Units”)
and, in connection therewith, has determined to issue and deliver up to 13,416,667 warrants (including up to 1,312,500 warrants subject
to the Over-allotment Option) to public investors in the Offering;


 


WHEREAS, the Company has filed with the U.S. Securities
and Exchange Commission (the “Commission”) a registration statement on Form S-1, File No. 333-254835 (the “Registration
Statement”) and prospectus (the “Prospectus”), for the registration, under the Securities Act of 1933, as
amended (the “Securities Act”), of the issuance of the Units, the Warrants and the Ordinary Shares included in the
Units;


 


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 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 (if a physical certificate is issued), 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 express terms and conditions set forth in
this Agreement.


 


2.             Warrants.


 


2.1           Form of Warrant. Each Warrant shall initially be issued in registered form only.


 


2.2           Effect of Countersignature. If a physical certificate is issued, unless and until countersigned by the Warrant Agent pursuant
to this Agreement, a certificated Warrant 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 the initial issuance of the Warrants and the registration of transfer of the Warrants. Upon the initial issuance of the Warrants in
book-entry form, 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. If requested, the Registered Holder of a
Warrant shall be issued a definitive certificate in physical form evidencing such Warrants which shall be in the form attached hereto
as Exhibit B.


 


Physical certificates, if issued, shall be signed
by, or bear the facsimile signature of, the Chairman of the board of directors of the Company (the “Board”), Chief
Executive Officer, Chief Financial Officer, the President or the 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.


 


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 any physical 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.


 






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3.             Terms
and Exercise of Warrants.


 


3.1           Warrant
Price. Each whole Warrant, when countersigned by the Warrant Agent, 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 Ordinary Shares stated therein, at the price of $11.50
per share, subject to the adjustments provided in Section 4 hereof and in the penultimate sentence of this Section 3.1.
The term “Warrant Price” as used in this Agreement shall mean the price per share at which each Ordinary Share 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. The term “Business Day” means
a day other than a Saturday, Sunday or federal holiday, on which banks in New York City are generally open for normal business.


 


3.2           Duration
of Warrants. A Warrant may be exercised only during the period (the “Exercise Period”) commencing on the later
of: (i) the date that is thirty (30) days after the first date on which the Company completes a merger, consolidation, share exchange,
asset acquisition, share purchase, reorganization or similar business combination, involving the Company and one or more businesses or
entities (a “Business Combination”), or (ii) the date that is twelve (12) months from the date of the closing of the
Offering and terminating at the earlier to occur of; (x) 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 and (y) the liquidation of the Company (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 hereof, with respect to an effective registration statement. Each Warrant not exercised on or
before the Expiration Date shall become null and 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, when countersigned by the Warrant Agent, may be exercised by
the Registered Holder thereof by surrendering it (if evidenced by definitive certificate) at the office of the Warrant Agent, or at
the office of its successor as Warrant Agent, in the Borough of Manhattan, City and State of New York, with the subscription form,
as set forth in the Warrant, duly executed, and by paying in full the Warrant Price for each full Ordinary Share 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 Ordinary Shares and the issuance of such Ordinary Share, as follows:


 


(a)       in lawful money of the United States, in good certified check or good bank draft payable to the Warrant Agent;


 


(b)       by
surrendering the Warrants for that number of Ordinary Shares equal to the quotient obtained by dividing (x) the product of the number
of Ordinary Shares underlying the Warrants, multiplied by the excess of the 10-Day Average Closing Price, as of the date prior to the
date on which notice of exercise is sent or given to the Warrant Agent, less the Warrant Price by (y) the 10-Day Average Closing Price.
 “10-Day Average Closing Price” means, as of any date, the average last reported sale price of the Ordinary Shares as
reported during the ten (10) trading day period ending on the trading day prior to such date. “Last Reported Sale Price”
shall mean the last reported sale price of the Ordinary Shares on the date prior to the date on which notice of exercise of the Warrant
is sent to the Warrant Agent; or


 


(c)       as
provided in Section 6.4 hereof.


 


3.3.2        Issuance
of Ordinary Shares 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) hereof), the Company shall issue to the
Registered Holder of such Warrant a book-entry position or certificate, as applicable, for the number of full Ordinary Shares 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 Ordinary
Shares as to which such Warrant shall not have been exercised. Notwithstanding the foregoing, the Company shall not be obligated to
deliver any Ordinary Shares 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 Ordinary Shares underlying the Warrants is then
effective and a prospectus relating thereto is current or a valid exemption from registration is available. No Warrant shall be
exercisable and the Company shall not be obligated to issue Ordinary Shares upon exercise of a Warrant unless the Ordinary Shares
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
Warrants shall have paid the full purchase price for the Unit solely for the Ordinary Shares underlying such Unit. In no event will
the Company be required to net cash settle the Warrant exercise. 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 an
Ordinary Share, the Company shall round down to the nearest whole number the number of Ordinary Shares to be issued to such holder.
Notwithstanding anything in this Agreement, for so long as any Warrant is held by APSG Sponsor III, L.P., such Warrant will not be
exercisable more than five (5) years from the effective date of the Registration Statement, in accordance with Financial Industry
Regulatory Authority, Inc. (“FINRA”) Rules. In addition, no such Warrant will contain terms which allow APSG Sponsor
III, L.P. to receive or accrue cash dividends prior to the exercise of the Warrants.


 






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3.3.3       
Valid Issuance. All Ordinary Shares 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 Ordinary Shares is
issued shall for all purposes be deemed to have become the holder of record of such Ordinary Shares 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 Ordinary Shares at the close of business on the next succeeding date on which the share transfer books or book-entry
system of the Warrant Agent 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 9.8%, or such other amount as a holder may specify (the “Maximum Percentage”) of
the Ordinary Shares outstanding immediately after giving effect to such exercise. For purposes of the foregoing sentence, the
aggregate number of Ordinary Shares beneficially owned by such person and its affiliates shall include the number of Ordinary Shares
issuable upon exercise of the Warrant with respect to which the determination of such sentence is being made, but shall exclude
Ordinary Shares 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 shares 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 issued and outstanding Ordinary Shares, the holder may rely on the number of
issued and outstanding Ordinary Shares 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 Ordinary
Shares issued and 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 Ordinary Shares then outstanding. In any
case, the number of issued and outstanding Ordinary Shares 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 issued and outstanding
Ordinary Shares 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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3.3.6        Lock-up of Private Placement Warrants.
The Warrants held by APSG Sponsor III, L.P. and the Ordinary Shares that are issuable upon exercise of such Warrants have been deemed
compensation by the FINRA and are therefore subject to a 180-day lock-up pursuant to FINRA Rule 5110(e)(1), commencing on the effective
date of the Registration Statement. Pursuant to FINRA Rule 5110(e)(1), these securities will not be sold during the Offering, or sold,
transferred, assigned, pledged, or hypothecated, or be the subject of any hedging, short sale, derivative, put or call transaction that
would result in the economic disposition of the securities by any person for a period of 180 days immediately following the effective
date of the Registration Statement or commencement of sales of the Offering, except to any underwriter and selected dealer participating
in the Offering and their bona fide officers or partners (provided that all securities so transferred remain subject to the lockup restriction
above for the remainder of the time period) or pursuant to another exception to the applicability of FINRA Rule 5110(e)(1).


 


4.             Adjustments.


 


4.1           Share Dividends.


 


4.1.1        Share
Dividends and Split-Ups. If after the date hereof, and subject to the provisions of Section 4.6 hereof, the number of
issued and outstanding Ordinary Shares is increased by a share dividend payable in Ordinary Shares, or by a split-up of Ordinary
Shares, or other similar event, then, on the effective date of such share dividend, split-up or similar event, the number of
Ordinary Shares issuable on exercise of each Warrant shall be increased in proportion to such increase in the issued and outstanding
Ordinary Shares. A rights offering to holders of Ordinary Shares entitling holders to purchase Ordinary Shares at a price less than
the “Fair Market Value” (as defined below) shall be deemed a share dividend of a number of Ordinary Shares equal
to the product of (i) the number of Ordinary Shares actually sold in such rights offering (or issuable under any other equity
securities sold in such rights offering that are convertible into or exercisable for the Ordinary Shares) multiplied by (ii) one (1)
minus the quotient of (x) the price per Ordinary Share paid in such rights offering divided by (y) the Fair Market Value. For
purposes of this subsection 4.1.1, if the rights offering is for securities convertible into or exercisable for Ordinary
Shares, in determining the price payable for the Ordinary Shares, there shall be taken into account any consideration received for
such rights, as well as any additional amount payable upon exercise or conversion. “Fair Market Value” means the
10-Day Average Closing Price as of the first (1st) date on which the Ordinary Shares trade on the applicable exchange or
in the applicable market, regular way, without the right to receive such rights. Notwithstanding anything to the contrary herein, no
Ordinary Shares shall be issued at less than their par value.


 






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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 Ordinary Shares on account of such Ordinary Shares (or
other shares of the Company’s share capital into which the Warrants are convertible), other than (a) as described in subsection
4.1.1 above, (b) Ordinary Cash Dividends (as defined below), (c) to satisfy the redemption rights of the holders of the Ordinary Shares
in connection with a proposed initial Business Combination, (d) to satisfy the redemption rights of the holders of Ordinary Shares in
connection with a shareholder vote to approve an amendment to the Company’s amended and restated memorandum and articles of association
to modify the substance or timing of the Company’s obligation to redeem 100% of the Ordinary Shares if the Company does not complete
its initial Business Combination within the period set forth in the Company’s amended and restated memorandum and articles of association,
or (e) in connection with the redemption of the Ordinary Shares included in the Units sold in the Offering upon the Company’s failure
to complete the Company’s initial Business Combination (any such non-excluded event being referred to herein as 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/or the fair market value (as determined by the Board, in good faith) of any securities or other assets
paid on each Ordinary Share in respect of such Extraordinary Dividend. For purposes of this subsection 4.1.2, “Ordinary
Cash Dividends” means any cash dividend or cash distribution which, when combined on a per share basis, with the per share amounts
of all other cash dividends and cash distributions paid on the Ordinary Shares during the 365-day period ending on the date of declaration
of such dividend or distribution (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 Ordinary
Shares issuable on exercise of each Warrant) does not exceed $0.50.


 


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


 


4.3           Adjustments
in Warrant Price. Whenever the number of Ordinary Shares purchasable upon the exercise of the Warrants is adjusted, as provided in
Section 4.1 or 4.2 hereof, 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 Ordinary Shares purchasable upon
the exercise of the Warrants immediately prior to such adjustment, and (y) the denominator of which shall be the number of Ordinary Shares
so purchasable immediately thereafter.


 






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4.4           Replacement
of Securities upon Reorganization, etc. In case of any reclassification or reorganization of the issued and outstanding Ordinary
Shares (other than a change covered by Section 4.1 or 4.2 hereof or that solely affects the par value of such Ordinary
Shares), or in the case of any merger or consolidation of the Company with or into another entity in which any “person” or
 “group” (as such terms are used in Section 13(d) and 14(d) of the Exchange Act) acquires more than 50% of the voting power
of the Company’s securities, 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, the holders of the Warrants 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 Ordinary Shares of the Company
immediately theretofore purchasable and receivable upon the exercise of the rights represented thereby, the kind and amount of shares
or other securities or property (including cash) receivable upon such reclassification, reorganization, merger or consolidation, that
the holder of the Warrants would have received if such holder had exercised his, her or its Warrant(s) immediately prior to such event
(the “Alternative Issuance”); provided, however, that if the holders of the Ordinary Shares were entitled
to exercise a right of election as to the kind or amount of securities, cash or other assets receivable upon such consolidation or merger,
then the kind and amount of securities, cash or other assets constituting the Alternative Issuance for which each Warrant shall become
exercisable shall be deemed to be the weighted average of the kind and amount received per share by the holders of the Ordinary Shares
in such consolidation or merger that affirmatively make such election; provided, further, that if less than seventy percent
(70%) of the consideration receivable by the holders of the Ordinary Shares in the applicable event is payable in the form of Ordinary
Shares in the successor entity that is listed for trading on a national securities exchange or is quoted in an established over-the-counter
market, or is to be so listed for trading or quoted immediately following such event, and if the Registered Holder properly exercises
the Warrant within thirty (30) days following the public disclosure of the consummation of such applicable event by the Company pursuant
to a current report on Form 8-K filed with the Commission, the Warrant Price shall be reduced by an amount (in dollars) equal to the
difference of (i) the Warrant Price in effect prior to such reduction minus (ii) (A) the Per Share Consideration (as defined below) (but
in no event less than zero) minus (B) the Black-Scholes Warrant Value (as defined below). The “Black-Scholes Warrant Value”
means the value of a Warrant immediately prior to the consummation of the applicable event based on the Black-Scholes Warrant Model for
an uncapped American Call on Bloomberg Financial Markets (“Bloomberg”), as calculated by an accounting, appraisal,
investment banking firm or consultant of nationally recognized standing that is, in the good faith judgment of the Board, qualified to
make such calculation. For purposes of calculating such amount, (1) the price of each Ordinary Share shall be the average last reported
sale price of the Ordinary Shares as reported during the ten (10) trading day period ending on the trading day prior to the applicable
event, (2) the assumed volatility shall be the ninety (90) day volatility obtained from the HVT function on Bloomberg determined as of
the trading day immediately prior to the day of the announcement of the applicable event, and (3) the assumed risk-free interest rate
shall correspond to the U.S. Treasury rate for a period equal to the remaining term of the Warrant. “Per Share Consideration”
means (i) if the consideration paid to holders of the Ordinary Shares consists exclusively of cash, the amount of such cash per Ordinary
Share, and (ii) in all other cases, the average last reported sale price of the Ordinary Shares as reported during the ten (10) trading
day period ending on the trading day prior to the effective date of the applicable event. If any reclassification or reorganization also
results in a change in Ordinary Shares covered by subsection 4.1.1 hereof, then such adjustment shall be made pursuant to subsection
4.1.1 or Sections 4.2, or 4.3 hereof 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.


 






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4.5           Notices
of Changes in Warrant. Upon every adjustment of the Warrant Price or the number of Ordinary 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 Ordinary 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; provided, however,
that no adjustment to the number of Ordinary Shares issuable upon exercise of a Warrant shall be required until cumulative adjustments
amount to one percent (1%) or more of the number of Ordinary Shares issuable upon exercise of a Warrant as last adjusted; provided,
further, that any such adjustments that are not made are carried forward and taken into account in any subsequent adjustment.
Notwithstanding the foregoing, all such carried forward adjustments shall be made (i) in connection with any subsequent adjustment that
(taken together with such carried forward adjustments) would result in a change of at least one percent (1%) in the number of Ordinary
Shares issuable upon exercise of a Warrant and (ii) on the exercise date of any Warrant. Upon the occurrence of any event specified in
Sections 4.1, 4.2, 4.3 or 4.4 hereof, the Company shall give written notice of the occurrence of such event
to each holder of a Warrant, 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 a fractional
Ordinary Share upon the 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 down to the nearest whole number the number of Ordinary Shares to be issued to such 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 Ordinary Shares as is stated in the Warrants
initially issued pursuant to this Agreement; provided, however, that 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.


 






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5.             Transfer
and Exchange of Warrants.


 


5.1           Transferability.
Subject to compliance with applicable law, the Warrants may be transferred, assigned or sold to any person.


 


5.2           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, 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.


 


5.3           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 in the event that
a Warrant surrendered for transfer bears a restrictive legend, 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.


 


5.4           Transfers
of Fractions of Warrants. The Warrant Agent shall not be required to effect any registration of transfer or exchange of Warrants
which would require the issuance of a Warrant certificate or book-entry position for a fraction of a Warrant.


 


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


 


5.6           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.


 


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


 


6.1           No Rights as Shareholder. A Warrant does not entitle the Registered Holder thereof to any of the rights of a shareholder
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 shareholder in respect of the meetings of shareholders or the election of directors of the
Company or any other matter.


 


6.2           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.


 






    10 


     


    

 


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


 


6.4           Registration
of the Ordinary Shares. The Company agrees that as soon as practicable, but in no event later than fifteen (15) Business Days after
the closing of its initial Business Combination, it shall use its commercially reasonable efforts to file with the Commission a registration
statement for the registration, under the Securities Act, of the Ordinary Shares issuable upon exercise of the Warrants. The Company
shall use its commercially reasonable efforts to cause the same to become effective and to maintain the effectiveness of such registration
statement, and a current prospectus relating thereto, until the expiration of the Warrants in accordance with the provisions of this
Agreement.


 


7.             Concerning
the Warrant Agent and Other Matters.


 


7.1           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 Ordinary Shares upon the exercise of the Warrants, but the Company and
the Warrant Agent shall not be obligated to pay any transfer taxes in respect of the Warrants or such Ordinary Shares.


 


7.2           Resignation, Consolidation, or Merger of Warrant Agent.


 


7.2.1        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 or other entity 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.


 






    11 


     


    

 


7.2.2       
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 Ordinary Shares not later than the effective date of any such
appointment.


 


7.2.3       
Merger or Consolidation of Warrant Agent. Any entity into which the Warrant Agent may be merged or with which it may be
consolidated or any entity 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.


 


7.3           Fees
and Expenses of Warrant Agent.


 


7.3.1       
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.


 


7.3.2       
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.


 


7.4           Liability of Warrant Agent.


 


7.4.1       
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 Chairman of the Board, Chief Executive Officer, Chief Financial Officer, the President or
the Secretary or other principal officer 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.


 


7.4.2       
Indemnity. The Warrant Agent shall be liable hereunder only for its own, or its representatives’, gross negligence,
willful misconduct, fraud, bad faith or material breach of this Agreement. The Company agrees to indemnify the Warrant Agent and save
it harmless against any and all liabilities, including judgments, out-of-pocket costs and reasonable outside 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 or its representatives’
gross negligence, willful misconduct, fraud, bad faith or material breach of this Agreement.


 


7.4.3        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 Ordinary Shares to be
issued pursuant to this Agreement or any Warrant or as to whether any Ordinary Shares shall, when issued, be valid and fully paid
and non-assessable.


 






    12 


     


    

 


7.5           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 Ordinary Shares through
the exercise of the Warrants.


 


7.6           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.


 


8.             Miscellaneous Provisions.


 


8.1           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.


 


8.2           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:


 


Apollo Strategic Growth Capital III


9 West 57th Street


43rd Floor


New York, NY 10019

Attention: James Crossen


Email: jcrossen@apollo.com


 


with a copy to (which shall not constitute notice):


 


Paul, Weiss, Rifkind, Wharton & Garrison LLP

1285 Avenue of the Americas

New York, NY 10019

Attention: Brian Janson


Email: bjanson@paulweiss.com


 






    13 


     


    

 


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 a copy to:


 


White & Case LLP


1221 Avenue of the Americas


New York, NY 10020

Attention: Joel L. Rubinstein

Email: joel.rubinstein@whitecase.com


 


8.3           Applicable
Law; Exclusive Forum. The validity, interpretation, and performance of this Agreement and of the Warrants shall be governed in
all respects by the laws of the State of New York, without giving effect to conflicts of law principles that would result in the
application of the substantive laws of another jurisdiction. Subject to applicable law, 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 Court for the Southern District of New York, and irrevocably submits to such
jurisdiction, which jurisdiction shall be exclusive forum for any such action, proceeding or claim. The Company hereby waives any
objection to such exclusive jurisdiction and that such courts represent an inconvenient forum. Notwithstanding the foregoing, the
provisions of this paragraph will not apply to suits brought to enforce any liability or duty created by the Exchange Act or any
other claim for which the federal district courts of the United States of America are the sole and exclusive forum. Any person or
entity purchasing or otherwise acquiring any interest in the Warrants shall be deemed to have notice of and to have consented to the
forum provisions in this Section 9.3. If any action, the subject matter of which is within the scope of the forum provisions
above, is filed in a court other than a court located within the State of New York or the United States District Court for the
Southern District of New York (a “foreign action”) in the name of any Warrant holder, such Warrant holder shall be
deemed to have consented to: (x) the personal jurisdiction of the state and federal courts located within the State of New York or
the United States District Court for the Southern District of New York in connection with any action brought in any such court to
enforce the forum provisions (an “enforcement action”), and (y) having service of process made upon such Warrant holder
in any such enforcement action by service upon such warrant holder’s counsel in the foreign action as agent for such warrant
holder.


 






    14 


     


    

 


8.4           Persons
Having Rights under this Agreement. Nothing in this Agreement shall be construed to confer upon, or give to, any person, corporation
or other entity 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.


 


8.5           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.


 


8.6           Counterparts;
Electronic Signatures. 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.
A signature to this Agreement transmitted electronically shall have the same authority, effect and enforceability as an original signature.


 


8.7           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.


 


8.8           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 (ii) adding or changing any 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 rights of the Registered Holders.
All other modifications or amendments, including any modification or amendment to increase the Warrant Price or shorten the Exercise
Period shall require the vote or written consent of the Registered Holders of fifty percent (50%) of the then outstanding 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 hereof, respectively, without the consent of the Registered Holders.


 


8.9           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.


 



Exhibit A – Legend


 






    15


     


    

 


Exhibit B – Form of Warrant Certificate


 









    16


     


    

 


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


 


	 	APOLLO STRATEGIC GROWTH CAPITAL III
	 	 
	 	By:	 
	 	 	Name: 	James Crossen
	 	 	Title:	Chief Financial Officer, Chief Accounting Officer and Secretary



 


[Signature Page to Warrant Agreement]


 






     


     


    

 


	 	CONTINENTAL STOCK TRANSFER & TRUST COMPANY, as Warrant Agent
	 	 
	 	By:	 
	 	 	Name: 	Henry Farrell
	 	 	Title:	Vice President


 


[Signature Page to Warrant Agreement]


 









     


     


    

 


EXHIBIT A



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 APOLLO STRATEGIC GROWTH CAPITAL III (THE “COMPANY”), APSG SPONSOR III, L.P. 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 SECTION 3 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.


 


SECURITIES EVIDENCED BY THIS CERTIFICATE AND ORDINARY SHARES 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.”


 






    A-1


     


    

 


EXHIBIT B




 


[Form of Warrant Certificate]


 


[FACE]


 


Number


 


Warrants


THIS WARRANT SHALL BE NULL AND VOID IF NOT
EXERCISED PRIOR TO THE EXPIRATION OF THE EXERCISE PERIOD PROVIDED FOR

IN THE WARRANT AGREEMENT DESCRIBED BELOW


APOLLO STRATEGIC GROWTH CAPITAL III


 


Incorporated Under the Laws of the Cayman Islands


 


CUSIP


 


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 Class A ordinary shares, $0.0001 par value per share (“Ordinary Shares”), of Apollo Strategic Growth
Capital III, a Cayman Islands exempted company and incorporated with limited liability (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 Ordinary Shares as set forth below, at the exercise price (the “Warrant
Price”) as determined pursuant to the Warrant Agreement, payable in lawful money of the United States of America upon surrender
of this Warrant Certificate and payment of the Warrant Price (or through “cashless exercise” as provided for
in the Warrant Agreement) 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 Ordinary Share. 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 an Ordinary Share, the Company will, upon exercise, round
down to the nearest whole number of the number of Ordinary Shares to be issued to the holder of the Warrant. The number of Ordinary Shares
issuable upon exercise of the Warrants is subject to adjustment upon the occurrence of certain events as set forth in the Warrant Agreement.


 


The initial Warrant Price per Ordinary Share for
any Warrant is equal to $11.50 per share. The Warrant Price is subject to adjustment upon the occurrence of certain events as 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 null and 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.


 


This Warrant Certificate shall be governed by and
construed in accordance with the internal laws of the State of New York, without regard to conflicts of laws principles thereof.


 


	 	APOLLO STRATEGIC GROWTH CAPITAL III
	 	 
	 	By:	 
	 	 	Name:	James Crossen
	 	 	Title:	Chief Financial Officer, Chief Accounting Officer and Secretary
	 	 	 
	 	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 Ordinary Shares and are issued or to be issued
pursuant to a Warrant Agreement dated as of [__], 2022 (the “Warrant Agreement”), duly executed and delivered
by the Company to Continental Stock Transfer & Trust Company, a New York corporation, as warrant agent (or successor warrant agent)
(collectively, 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 Ordinary
Shares to be issued upon exercise is effective under the Securities Act and (ii) a prospectus thereunder relating to the Ordinary Shares
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 Ordinary Shares issuable upon exercise of the Warrants and the Warrant Price 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 an Ordinary Share, the Company shall, upon exercise, round down to the nearest whole number of Ordinary Shares 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 shareholder 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                Ordinary Shares and herewith tenders payment for such Ordinary Shares
to the order of Apollo Strategic Growth Capital III (the “Company”) in the amount of $                  in accordance with
the terms hereof. The undersigned requests that a certificate for such Ordinary Shares be registered in the name of                   , whose address
is                    and that such Ordinary Shares be delivered to                    whose address is                   . If said number of Ordinary Shares is less than all of
the Ordinary Shares purchasable hereunder, the undersigned requests that a new Warrant Certificate representing the remaining balance
of such Ordinary Shares 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 is to be exercised
on a “cashless” basis pursuant to Section 3.3.1(b) of the Warrant Agreement, the number of Ordinary Shares
that this Warrant is exercisable for shall be determined in accordance with 3.3.1(b) 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 Ordinary Shares
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 Ordinary Shares 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 Ordinary Shares. If said number of Ordinary
Shares is less than all of the Ordinary Shares purchasable hereunder (after giving effect to the cashless exercise), the undersigned requests
that a new Warrant Certificate representing the remaining balance of such Ordinary Shares 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 SECURITIES AND EXCHANGE COMMISSION RULE 17Ad-15 (OR ANY SUCCESSOR RULE) UNDER THE SECURITIES EXCHANGE ACT OF 1934, AS AMENDED).