Exhibit 10.3


FORM OF INVESTMENT MANAGEMENT TRUST
AGREEMENT


This Investment Management Trust Agreement
(this “Agreement”) is made effective as of [____], 2022 by and between Apollo Strategic Growth Capital
III, a Cayman Islands exempted company, incorporated with limited liability (the “Company”), and Continental
Stock Transfer & Trust Company, a New York corporation (the “Trustee”).


WHEREAS, the Company’s registration
statement on Form S-1, File No. 333-254835 (the “Registration Statement”) and prospectus (the “Prospectus”)
for the initial public offering of the Company’s units (the “Units”), each of which consists of
one Class A ordinary share, par value $0.0001 per share, of the Company (each an “Ordinary Share”), and
a fraction of one redeemable warrant of the Company, each whole warrant entitling the holder thereof to purchase one Ordinary Share
(such initial public offering hereinafter referred to as the “Offering”), has been declared effective
as of the date hereof by the U.S. Securities and Exchange Commission; and


WHEREAS, the Company has entered into an
Underwriting Agreement (the “Underwriting Agreement”) with Credit Suisse Securities (USA) LLC, as
representative (the “Representative”) of the several underwriters named therein (the
 “Underwriters”); and


WHEREAS, as described in the Registration
Statement, an aggregate of $350,000,000 from the gross proceeds of the Offering and sale of the Private Placement Warrants (as
defined in the Underwriting Agreement) (or $402,500,000 if the Underwriters’ over-allotment option is exercised in full)
will be delivered to the Trustee to be deposited and held in a segregated trust account located at all times in the United States
(the “Trust Account”) for the benefit of the Company and the holders of the Ordinary Shares included
in the Units issued in the Offering as hereinafter provided (the amount to be delivered to the Trustee (and any interest subsequently
earned thereon) is referred to herein as the “Property,” the shareholders for whose benefit the Trustee
shall hold the Property will be referred to as the “Public Shareholders,” and the Public Shareholders
and the Company will be referred to together as the “Beneficiaries”); and


WHEREAS, pursuant to the Underwriting Agreement,
a portion of the Property equal to $12,250,000, or $14,087,500 if the Underwriters’ over-allotment option is exercised in
full, is attributable to deferred underwriting discounts and commissions that will be payable by the Company to the Underwriters
upon and concurrently with the consummation of the Business Combination (as defined below) (the “Deferred Discount”);
and


WHEREAS, the Company and the Trustee desire
to enter into this Agreement to set forth the terms and conditions pursuant to which the Trustee shall hold the Property.




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NOW THEREFORE, IT IS AGREED:


1.              Agreements and Covenants of Trustee. The Trustee hereby agrees and covenants to:


(a)               
Hold the Property in trust for the Beneficiaries in accordance with the terms of this Agreement in the Trust Account established
by the Trustee in the United States at J.P. Morgan Chase Bank, N.A. (or at another U.S.-chartered commercial bank with consolidated
assets of $100 billion or more) and at a brokerage institution selected by the Trustee that is reasonably satisfactory to the Company;


(b)              
Manage, supervise and administer the Trust Account subject to the terms and conditions set forth herein;


(c)               
In a timely manner, upon the written instruction of the Company, invest and reinvest the Property in solely United States
government securities within the meaning of Section 2(a)(16) of the Investment Company Act of 1940, as amended, having a maturity
of 185 days or less, or in money market funds meeting the conditions of paragraphs (d)(1), (d)(2), (d)(3) and (d)(4) of Rule 2a-7
promulgated under the Investment Company Act of 1940, as amended (or any successor rule), which invest only in direct U.S. government
treasury obligations, as determined by the Company; the Trustee may not invest in any other securities or assets, it being understood
that the Trust Account will earn no interest while account funds are uninvested awaiting the Company’s instructions hereunder
and the Trustee may earn bank credits or other consideration;


(d)              
Collect and receive, when due, all interest or other income arising from the Property, which shall become part of the “Property,”
as such term is used herein;


(e)               
Promptly notify the Company of all communications received by the Trustee with respect to any Property requiring action
by the Company;


(f)               
Supply any necessary information or documents as may be requested by the Company (or its authorized agents) in connection
with the Company’s preparation of the tax returns relating to assets held in the Trust Account;


(g)              
Participate in any plan or proceeding for protecting or enforcing any right or interest arising from the Property if, as
and when instructed by the Company to do so;


(h)              
Render to the Company monthly written statements of the activities of, and amounts in, the Trust Account reflecting all
receipts and disbursements of the Trust Account;




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 (i)                 
Commence liquidation of the Trust Account only after and promptly after (x) receipt of, and only in accordance with, the terms of a
letter from the Company (“Termination Letter”) in a form substantially similar to that attached hereto as
either Exhibit A or Exhibit B, as applicable, signed on behalf of the Company by its Chief Executive Officer,
President, Chief Financial Officer, Secretary or Chairman of the board of directors of the Company (the
 “Board”) or other authorized officer of the Company, and, in the case of Exhibit A, acknowledged by
the Representative and complete the liquidation of the Trust Account and distribute the Property in the Trust Account, including
interest earned on the funds held in the Trust Account (net of amounts withdrawn in accordance with this Agreement and less up to
$100,000 of interest that may be released to the Company to pay dissolution expenses), only as directed in the Termination Letter
and the other documents referred to therein, or (y) upon the date which is the later of (1) 21 months after the closing of the
Offering (or up to 24 months from the closing of the Offering if the Company extends the period of time to consummate an initial
Business Combination) and (2) such later date as may be approved by the Company’s shareholders in accordance with the Company’s
amended and restated memorandum and articles of association, if a Termination Letter has not been received by the Trustee prior to
such date, in which case the Trust Account shall be liquidated in accordance with the procedures set forth in the Termination Letter
attached as Exhibit B and the Property in the Trust Account, including interest earned on the funds held in the Trust Account
(net of amounts withdrawn in accordance with this Agreement and less up to $100,000 of interest that may be released to the Company
to pay dissolution expenses), shall be distributed to the Public Shareholders of record as of such date;


(j)                
Upon written request from the Company, which may be given from time to time in a form substantially similar to that attached
hereto as Exhibit C (a “Tax Payment Withdrawal Instruction”), withdraw from the Trust Account
and distribute to the Company the amount of interest earned on the Property requested by the Company to cover any tax obligation
owed by the Company as a result of assets of the Company or interest or other income earned on the Property, which amount shall
be delivered directly to the Company, and the Company shall forward such amount to the relevant taxing authority; provided,
however, that to the extent there is not sufficient cash in the Trust Account to pay such tax obligation, the Trustee shall
liquidate such assets held in the Trust Account as shall be designated by the Company in writing to make such distribution, so
long as there is no reduction in the principal amount per share initially deposited in the Trust Account. The written request of
the Company referenced above shall constitute presumptive evidence that the Company is entitled to said funds, and the Trustee
shall have no responsibility to look beyond said request;


(k)              
[Reserved];


(l)                
Upon written request from the Company, which may be given from time to time in a form substantially similar to that attached
hereto as Exhibit D (a “Shareholder Redemption Withdrawal Instruction”), the Trustee shall distribute
to the Public Shareholders on behalf of the Company the amount requested by the Company to be used to redeem Ordinary Shares from
Public Shareholders properly submitted in connection with a shareholder vote to approve an amendment to the Company’s amended
and restated memorandum and articles of association that would affect the substance or timing of the Company’s obligation
to redeem 100% of its Ordinary Shares if the Company has not consummated an initial Business Combination within such time as is
described in the Company’s amended and restated memorandum and articles of association or with respect to any other material
provisions relating to shareholders’ rights or pre-initial Business Combination activity. The written request of the Company
referenced above shall constitute presumptive evidence that the Company is entitled to distribute said funds, and the Trustee shall
have no responsibility to look beyond said request; and




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 (m)            
 Not make any withdrawals or distributions from the Trust Account other than pursuant to Section 1(i), 1(j),
1(k) or 1(l) above.


2.             
Agreements and Covenants of the Company. The Company hereby agrees and covenants to:


(a)               
Give all instructions to the Trustee hereunder in writing, signed by the Company’s Chairman of the Board, President,
Chief Executive Officer, Chief Financial Officer or Secretary. In addition, except with respect to its duties under Sections
1(i), 1(j), 1(k) and 1(l) hereof, the Trustee shall be entitled to rely on, and shall be protected in relying
on, any verbal or telephonic advice or instruction which it, in good faith and with reasonable care, believes to be given by any
one of the persons authorized above to give written instructions, provided that the Company shall promptly confirm such
instructions in writing;


(b)              
Subject to Section 4 hereof, hold the Trustee harmless and indemnify the Trustee from and against any and all expenses,
including reasonable counsel fees and disbursements, or losses suffered by the Trustee in connection with any action taken by it
hereunder and in connection with any action, suit or other proceeding brought against the Trustee involving any claim, or in connection
with any claim or demand, which in any way arises out of or relates to this Agreement, the services of the Trustee hereunder, or
the Property or any interest earned on the Property, except for expenses and losses resulting from the Trustee’s, or its
representatives’, gross negligence, fraud or willful misconduct. Promptly after the receipt by the Trustee of notice of demand
or claim or the commencement of any action, suit or proceeding, pursuant to which the Trustee intends to seek indemnification under
this Section 2(b), it shall notify the Company in writing of such claim (hereinafter referred to as the “Indemnified
Claim”). The Trustee shall have the right to conduct and manage the defense against such Indemnified Claim; provided
that the Trustee shall obtain the consent of the Company with respect to the selection of counsel; provided, further
that the Company may conduct and manage the defense against any Indemnified Claim if the Trustee does not promptly take reasonable
steps to mount such a defense. The Trustee may not agree to settle any Indemnified Claim without the prior written consent of the
Company. The Company may participate in any such action with its own counsel;


(c)               
Pay the Trustee the fees set forth on Schedule A hereto, including an initial set-up fee, annual administration fee,
and transaction processing fee which fees shall be subject to modification by the parties from time to time. It is expressly understood
that the Property shall not be used to pay such fees unless and until it is distributed to the Company pursuant to Section 1(i)
hereof. The Company shall pay the Trustee the initial set-up fee and the first annual administration fee at the consummation of
the Offering. The Trustee shall refund to the Company the annual administration fee (on a pro rata basis) with respect to any period
after the liquidation of the Trust Account. The Company shall not be responsible for any other fees or charges of the Trustee except
as set forth in this Section 2(c), Schedule A and as may be provided in Section 2(b) hereof;




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(d)               
In connection with any vote of the Company’s shareholders regarding a merger, consolidation, share exchange, asset
acquisition, share purchase, reorganization or similar business combination involving the Company and one or more businesses (the
 “Business Combination”), provide to the Trustee an affidavit or certificate of the inspector of elections
for the shareholder meeting verifying the vote of such shareholders regarding such Business Combination;


(e)               
Provide the Representative with a copy of any Termination Letter(s) and/or any other correspondence that is sent to the
Trustee with respect to any proposed withdrawal from the Trust Account promptly after it issues the same;


(f)               
Unless otherwise agreed between the Company and the Representatives ensure that any Instruction Letter delivered in connection
with a Termination Letter in the form of Exhibit A expressly provides that the Deferred Discount is paid directly to the
accounts as directed by the Representative prior to any transfer of the funds held in the Trust Account to the Company or any other
person;


(g)              
Instruct the Trustee to make only those distributions that are permitted under this Agreement, and refrain from instructing
the Trustee to make any distributions that are not permitted under this Agreement; and


(h)              
Within four (4) business days after the Underwriters exercise the over-allotment option (or any unexercised portion thereof)
or such over-allotment option expires, provide the Trustee with a notice in writing of the total amount of the Deferred Discount,
which shall in no event be less than $12,250,000, or $14,087,500 if the Underwriters’ over-allotment option is exercised
in full.


3.             
Limitations of Liability. The Trustee shall have no responsibility or liability to:


(a)               
Imply obligations, perform duties, inquire or otherwise be subject to the provisions of any agreement or document other
than this Agreement and that which is expressly set forth herein;


(b)              
Take any action with respect to the Property, other than as directed in Section 1 hereof, and the Trustee shall have
no liability to any third party except for liability arising out of the Trustee’s, or its representatives’, gross negligence,
fraud or willful misconduct;


(c)               
Institute any proceeding for the collection of any principal and income arising from, or institute, appear in or defend
any proceeding of any kind with respect to, any of the Property unless and until it shall have received instructions from the Company
given as provided herein to do so and the Company shall have advanced or guaranteed to it funds sufficient to pay any reasonably
incurred expenses incident thereto;


(d)              
Refund any depreciation in principal of any Property;




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(e)               
 Assume that the authority of any person designated by the Company to give instructions hereunder shall not be continuing
unless provided otherwise in such designation, or unless the Company shall have delivered a written revocation of such authority
to the Trustee;


(f)               
The other parties hereto or to anyone else for any action taken or omitted by it, or any action suffered by it to be taken
or omitted, in good faith and in the Trustee’s best judgment, except for the Trustee’s, or its representatives’,
gross negligence, fraud or willful misconduct. The Trustee may rely conclusively and shall be protected in acting upon any order,
notice, demand, certificate, opinion or advice of counsel (including counsel chosen by the Trustee, which counsel may be the Company’s
counsel), statement, instrument, report or other paper or document (not only as to its due execution and the validity and effectiveness
of its provisions, but also as to the truth and acceptability of any information therein contained) which the Trustee believes,
in good faith and with reasonable care, to be genuine and to be signed or presented by the proper person or persons. The Trustee
shall not be bound by any notice or demand, or any waiver, modification, termination or rescission of this Agreement or any of
the terms hereof, unless evidenced by a written instrument delivered to the Trustee, signed by the proper party or parties and,
if the duties or rights of the Trustee are affected, unless it shall give its prior written consent thereto;


(g)              
Verify the accuracy of the information contained in the Registration Statement;


(h)              
Provide any assurance that any Business Combination entered into by the Company or any other action taken by the Company
is as contemplated by the Registration Statement;


(i)                
File information returns with respect to the Trust Account with any local, state or federal taxing authority or provide
periodic written statements to the Company documenting the taxes payable by the Company, if any, relating to any interest income
earned on the Property;


(j)                
Prepare, execute and file tax reports, income or other tax returns and pay any taxes with respect to any income generated
by, and activities relating to, the Trust Account, regardless of whether such tax is payable by the Trust Account or the Company,
including, but not limited to, tax obligations, except pursuant to Section 1(j) hereof; or


(k)              
Verify calculations, qualify or otherwise approve the Company’s written requests for distributions pursuant to Sections
1(i), 1(j), 1(k) or 1(l) hereof.


4.             
Trust Account Waiver. The Trustee has no right of set-off or any right, title, interest or claim of any kind (“Claim”)
to, or to any monies in, the Trust Account, and hereby irrevocably waives any Claim to, or to any monies in, the Trust Account
that it may have now or in the future. In the event the Trustee has any Claim against the Company under this Agreement, including,
without limitation, under Section 2(b) or Section 2(c) hereof, the Trustee shall pursue such Claim solely against
the Company and its assets outside the Trust Account and not against the Property or any monies in the Trust Account.




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 5.             Termination. This Agreement shall terminate as follows:


(a)               
If the Trustee gives written notice to the Company that it desires to resign under this Agreement, the Company shall use
its reasonable efforts to locate a successor trustee, pending which the Trustee shall continue to act in accordance with this Agreement.
At such time that the Company notifies the Trustee that a successor trustee has been appointed and has agreed to become subject
to the terms of this Agreement, the Trustee shall transfer the management of the Trust Account to the successor trustee, including
but not limited to the transfer of copies of the reports and statements relating to the Trust Account and any other reasonable
transfer requests that the Company may make, whereupon this Agreement shall terminate; provided, however, that in
the event that the Company does not locate a successor trustee within ninety (90) days of receipt of the resignation notice from
the Trustee, the Trustee may submit an application to have the Property deposited with any court in the State of New York or with
the United States District Court for the Southern District of New York and upon such deposit, the Trustee shall be immune from
any liability whatsoever; or


(b)              
At such time that the Trustee has completed the liquidation of the Trust Account and its obligations in accordance with
the provisions of Section 1(i) hereof and distributed the Property in accordance with the provisions of the Termination
Letter, this Agreement shall terminate except with respect to Section 2(b).


6.             
Miscellaneous.


(a)               
The Company and the Trustee each acknowledge that the Trustee will follow the security procedures set forth below with respect
to funds transferred from the Trust Account. The Company and the Trustee will each restrict access to confidential information
relating to such security procedures to authorized persons. Each party must notify the other party immediately if it has reason
to believe unauthorized persons may have obtained access to such confidential information, or of any change in its authorized personnel.
In executing funds transfers, the Trustee shall rely upon all information supplied to it by the Company, including, account names,
account numbers, and all other identifying information relating to a Beneficiary, Beneficiary’s bank or intermediary bank.
Except for any liability arising out of the Trustee’s, or its representatives’, gross negligence, fraud or willful
misconduct, the Trustee shall not be liable for any loss, liability or expense resulting from any error in the information or transmission
of the funds.


(b)              
This Agreement shall be governed by and construed and enforced in accordance with 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.
This Agreement may be executed in several original or facsimile counterparts, each one of which shall constitute an original, and
together shall constitute but one instrument.




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 (c)               
 This Agreement contains the entire agreement and understanding of the parties hereto with respect to the subject matter
hereof. Except for Sections 1(i), 1(j), 1(k) and 1(l) hereof (which sections may only be changed,
amended or modified with the affirmative vote of at least sixty-five percent (65%) of the then issued and outstanding Ordinary
Shares and Class B ordinary shares, par value $0.0001 per share, of the Company voting together as a single class; provided that
no such amendment will affect any Public Shareholder who has otherwise indicated his, her or its election to redeem his, her or
its Ordinary Shares in connection with a shareholder vote to approve an amendment to the Company’s amended and restated
memorandum and articles of association), this Agreement or any provision hereof may only be changed, amended or modified (other
than to correct a typographical error) by a writing signed by each of the parties hereto. Except for any liability arising out
of the Trustee’s, or its representatives’, gross negligence, fraud or willful misconduct, the Trustee may rely conclusively
on the certification from the inspector or elections referenced above and shall be relieved of all liability to any party for
executing the proposed amendment in reliance thereon.


(d)              
The parties hereto consent to the jurisdiction and venue of any state or federal court located in the City of New York County,
County of New York, State of New York, for purposes of resolving any disputes hereunder. AS TO ANY CLAIM, CROSS-CLAIM OR COUNTERCLAIM
IN ANY WAY RELATING TO THIS AGREEMENT, EACH PARTY WAIVES THE RIGHT TO TRIAL BY JURY.


(e)               
Any notice, consent or request to be given in connection with any of the terms or provisions of this Agreement shall be
in writing and shall be sent by express mail or similar private courier service, by certified mail (return receipt requested),
by hand delivery or by facsimile or email transmission:


if to the Trustee, to:


Continental Stock Transfer & Trust Company

One State Street


30th Floor


New York, New York 10004

Attn: Francis Wolf and Celeste Gonzalez

Email: fwolf @continentalstock.com


              cgonzalez@continentalstock.com


 


if to the Company, to:


Apollo Strategic Growth Capital III

9 West 57th Street, 43rd Floor

New York, NY 10019

Attn: Chief Financial Officer

Email: jcrossen@apollo.com




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in each case, with copies to:


Paul, Weiss, Rifkind, Wharton & Garrison LLP

1285 Avenue of the Americas


New York, NY 10019

Attn: Brian M. Janson, Esq.

Email: bjanson@paulweiss.com


and


[___]


[___]


[___]


Attn:


Email:


and


White & Case LLP

1221 Avenue of the Americas


New York, NY 10020

Attn: Joel L. Rubinstein, Esq. and Daniel E. Nussen, Esq.

Email: joel.rubinstein@whitecase.com and daniel.nussen@whitecase.com


(f)               
This Agreement may not be assigned by the Trustee without the prior consent of the Company.


(g)              
Each of the Company and the Trustee hereby represents that it has the full right and power and has been duly authorized
to enter into this Agreement and to perform its respective obligations as contemplated hereunder. The Trustee acknowledges and
agrees that it shall not make any claims or proceed against the Trust Account, including by way of set-off, and shall not be entitled
to any funds in the Trust Account under any circumstance.


(h)              
This Agreement is the joint product of the Trustee and the Company and each provision hereof has been subject to the mutual
consultation, negotiation and agreement of such parties and shall not be construed for or against any party hereto.


(i)                
This Agreement may be executed in any number of counterparts, each of which shall be deemed to be an original, but all such
counterparts shall together constitute one and the same instrument. Delivery of a signed counterpart of this Agreement by facsimile
or electronic transmission shall constitute valid and sufficient delivery thereof.


(j)                
Each of the Company and the Trustee hereby acknowledges and agrees that the Representative, on behalf of the Underwriters,
is a third party beneficiary of this Agreement.




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(k)              
 The Trustee shall perform its duties under this Agreement in compliance with all applicable laws, including those relating
to privacy, data protection and information security, shall keep confidential all information relating to this Agreement and, except
as required by applicable law, shall not use such information for any purpose other than the performance of the Trustee’s
obligations under this Agreement.


(l)                
Except as specified herein, no party to this Agreement may assign its rights or delegate its obligations hereunder to any
other person or entity.


[Signature Page Follows]


 




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IN WITNESS WHEREOF, the parties have
duly executed this Investment Management Trust Agreement as of the date first written above.


 


	 	Continental Stock Transfer & Trust Company, as Trustee
	 	 	 
	 	By:	 
	 	 	Name:
	 	 	Title:
	 	 	 
	 	Apollo Strategic Growth Capital III
	 	 	 
	 	By:	
	 	 	Name: James Crossen 
	 	 	Title: Chief Financial Officer, Chief Accounting Officer and Secretary


 


[Signature page to Investment Management
Trust Agreement]


 




    	  



    	 



    

SCHEDULE A


 


	Fee Item	 	Time and method of payment	 	Amount	 
	Initial set-up fee.	 	Initial closing of Offering by wire transfer.	 	$	3,500.00	 
	Trustee administration fee	 	Payable annually. First year fee payable at initial closing of Offering by wire transfer; thereafter, payable by wire transfer or check.	 	$	10,000.00	 
	Transaction processing fee for disbursements to Company under Sections 1(i), 1(j), 1(k) and 1(l)	 	Billed to Company under Section 1	 	$	250.00	 
	Paying Agent services as required pursuant to Section 1(i) and 1(l)	 	Billed to Company upon delivery of service pursuant to Section 1(i) and 1(l)	 	 	Prevailing rates	 
	 	 	 	 	 	 	 




    	  



    	 



    

Exhibit
A

[Letterhead of Company]

[Insert date]


Continental Stock Transfer & Trust Company


1 State Street, 30th Floor


New York, New York 10004

Attn: Francis Wolf & Celeste Gonzalez


Re:Trust Account - Termination Letter


Dear Mr. Wolf and Ms. Gonzalez:


Pursuant to Section 1(i) of the
Investment Management Trust Agreement between Apollo Strategic Growth Capital III (the “Company”) and
Continental Stock Transfer & Trust Company (the “Trustee”), dated as of [___], 2022 (the “Trust
Agreement”), this is to advise you that the Company has entered into an agreement with [_] (the “Target
Business”) to consummate a business combination with Target Business (the “Business Combination”)
on or about [_], 20[_].The Company shall notify you at least seventy-two (72) hours in advance of the actual date of the consummation
of the Business Combination (the “Consummation Date”). Capitalized terms used but not defined herein
shall have the meanings set forth in the Trust Agreement.


In accordance with the terms of the Trust
Agreement, we hereby authorize you to commence to liquidate all of the assets of the Trust Account, and to transfer the proceeds
into the trust operating account at J.P. Morgan Chase Bank, N.A. to the effect that, on the Consummation Date, all of the funds
held in the Trust Account will be immediately available for transfer to the account or accounts that the Company shall direct on
the Consummation Date (including as directed to it by the Representative with respect to the Deferred Discount). It is acknowledged
and agreed that while the funds are on deposit in the trust operating account at J.P. Morgan Chase Bank, N.A. awaiting distribution,
the Company will not earn any interest or dividends.


On the Consummation Date (i) counsel for
the Company shall deliver to you written notification that the Business Combination has been consummated, or will be consummated
substantially concurrently with your transfer of funds to the accounts as directed by the Company (the “Notification”)
and (ii) the Company shall deliver to you (a) a certificate of the Chief Executive Officer of the Company, which verifies that
the Business Combination has been approved by a vote of the Company’s shareholders, if a vote is held and (b) a joint written
instruction signed by the Company and the Representative with respect to the transfer of the funds held in the Trust Account, including
payment of amounts owed to public shareholders who have properly exercised their redemption rights and payment of the Deferred
Discount from the Trust Account directly to the account or accounts directed by the Representative (the “Instruction
Letter”). You are hereby directed and authorized to transfer the funds held in the Trust Account immediately upon
your receipt of the Notification and the Instruction Letter, in accordance with the terms of the Instruction Letter. In the event
that certain deposits held in the Trust Account may not be liquidated by the Consummation Date without penalty, you will notify
the Company in writing of the same and the Company shall direct you as to whether such funds should remain in the Trust Account
and be distributed after the Consummation Date to the Company. Upon the distribution of all the funds, net of any payments necessary
for reasonable unreimbursed expenses related to liquidating the Trust Account, your obligations under the Trust Agreement shall
be terminated.




    A-1


     


    

 


In the event that the Business Combination
is not consummated on the Consummation Date described in the notice thereof and we have not notified you on or before the original
Consummation Date of a new Consummation Date, then upon receipt by the Trustee of written instructions from the Company, the funds
held in the Trust Account shall be reinvested as provided in Section 1(c) of the Trust Agreement on the business day immediately
following the Consummation Date as set forth in such written instructions as soon thereafter as possible.


	 	Very truly yours,
	 	 
	 	Apollo Strategic Growth Capital III
	 	 	 
	 	By:	 
	 	 	Name:
	 	 	Title:


Acknowledged:


 


[_____]


 


 


	By:	 
	 	Name:
	 	Title:


 


 


 


 




    A-2


     


    

EXHIBIT B

[Letterhead of Company]

[Insert date]


Continental Stock Transfer & Trust Company


1 State Street, 30th Floor


New York, New York 10004

Attn: Francis Wolf & Celeste Gonzalez


Re:    Trust Account -Termination Letter


Dear Mr. Wolf and Ms. Gonzalez:


Pursuant to Section 1(i) of the
Investment Management Trust Agreement between Apollo Strategic Growth Capital III (the “Company”) and
Continental Stock Transfer & Trust Company (the “Trustee”), dated as of [___], 2022 (the “Trust
Agreement”), this is to advise you that the Company has been unable to effect a business combination with a Target
Business within the time frame specified in the Company’s amended and restated memorandum and articles of incorporation,
as described in the Company’s Prospectus relating to the Offering. Capitalized terms used but not defined herein shall have
the meanings set forth in the Trust Agreement.


In accordance with the terms of the Trust
Agreement, we hereby authorize you to liquidate all of the assets in the Trust Account and to transfer the total proceeds into
the trust operating account at J.P. Morgan Chase Bank, N.A. to await distribution to the Public Shareholders. The Company has selected
[_], 20[_] as the record date for the purpose of determining the Public Shareholders entitled to receive their share of the liquidation
proceeds. You agree to be the Paying Agent of record and, in your separate capacity as Paying Agent, agree to distribute said funds
directly to the Public Shareholders in accordance with the terms of the Trust Agreement and the amended and restated memorandum
and articles of association of the Company. Upon the distribution of all the funds, net of any payments necessary for reasonable
unreimbursed expenses related to liquidating the Trust Account, your obligations under the Trust Agreement shall be terminated,
except to the extent otherwise provided in Section 1(i) of the Trust Agreement.


	 	Very truly yours,
	 	 
	 	Apollo Strategic Growth Capital III
	 	 	 
	 	By:	 
	 	 	Name: 
	 	 	Title:


 


cc:     [_____]


 


 




    B-1


     


    

EXHIBIT C

[Letterhead of Company]

[Insert date]


Continental Stock Transfer & Trust Company


1 State Street, 30th Floor


New York, New York 10004

Attn: Francis Wolf & Celeste Gonzalez


 


Re:        Trust Account - Tax Payment Withdrawal
Instruction


Dear Mr. Wolf and Ms. Gonzalez:


Pursuant to Section 1(j) of the
Investment Management Trust Agreement between Apollo Strategic Growth Capital III (the “Company”) and
Continental Stock Transfer & Trust Company (the “Trustee”), dated as of [___], 2022 (the “Trust
Agreement”), the Company hereby requests that you deliver to the Company $[_] of the interest income earned on the
Property as of the date hereof. Capitalized terms used but not defined herein shall have the meanings set forth in the Trust Agreement.


The Company needs such funds [to pay for
the tax obligations as set forth on the attached tax return or tax statement]. In accordance with the terms of the Trust Agreement,
you are hereby directed and authorized to transfer (via wire transfer) such funds promptly upon your receipt of this letter to
the Company’s operating account at:


[WIRE INSTRUCTION INFORMATION]


	 	Very truly yours,
	 	 
	 	Apollo Strategic Growth Capital III
	 	 	 
	 	By:	 
	 	 	Name: 
	 	 	Title: 


 


cc:      [_____]


 


 


 




    C-1


     


    

EXHIBIT D

[Letterhead of Company]

[Insert date]


Continental Stock Transfer & Trust Company


1 State Street, 30th Floor


New York, New York 10004

Attn: Francis Wolf & Celeste Gonzalez


Re:         Trust Account - Shareholder Redemption
Withdrawal Instruction


 


Dear Mr. Wolf and Ms. Gonzalez:


Pursuant to Section 1(l) of the
Investment Management Trust Agreement between Apollo Strategic Growth Capital III (the “Company”) and
Continental Stock Transfer & Trust Company (the “Trustee”), dated as of [___], 2022 (the “Trust
Agreement”), the Company hereby requests that you deliver $ [_] of the principal and interest income earned on the
Property as of the date hereof into a segregated account held by you on behalf of the Beneficiaries for distribution to the Public
Shareholders who have requested redemption of their shares. Capitalized terms used but not defined herein shall have the meanings
set forth in the Trust Agreement.


The Company needs such funds to pay its
Public Shareholders who have properly elected to have their Ordinary Shares redeemed by the Company in connection with a shareholder
vote to approve an amendment to the Company’s amended and restated memorandum and articles of association. As such, you are
hereby directed and authorized to transfer (via wire transfer) such funds promptly upon your receipt of this letter.


	 	Very truly yours,
	 	 
	 	Apollo Strategic Growth Capital III
	 	 	 
	 	By:	 
	 	 	Name: 
	 	 	Title: 


 


cc:      [_____]


 


 



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