Exhibit 10.2


[___], 2022


Apollo Strategic Growth Capital III

9 West 57th Street, 43rd Floor


New York, NY 10019




Re: Initial Public Offering


Ladies and Gentlemen:


This letter (this “Letter Agreement”)
is being delivered to you in accordance with the Underwriting Agreement (the “Underwriting Agreement”)
entered into by and between Apollo Strategic Growth Capital III, a Cayman Islands exempted company, incorporated with limited liability
(the “Company”), and Credit Suisse Securities (USA) LLC, as representative (the “Representative”) of the
several underwriters (each, an “Underwriter” and collectively, the “Underwriters”),
relating to an underwritten initial public offering (the “Public Offering”) of 35,000,000 of the Company’s
units (including up to 5,250,000 units that may be purchased to cover over-allotments, if any) (the “Units”),
each comprised of one Class A ordinary share of the Company, par value $0.0001 per share (the “Ordinary Shares”),
and one-third (1/3) of one redeemable Warrant. Each whole Warrant (each, a “Warrant”) entitles the holder
thereof to purchase one Ordinary Share at a price of $11.50 per share, subject to adjustment as described in the Prospectus (as
defined below). The Units will be sold in the Public Offering pursuant to a registration statement on Form S-1 and prospectus (the
 “Prospectus”) filed by the Company with the U.S. Securities and Exchange Commission (the “Commission”)
and the Company has applied to have the Units listed on the New York Stock Exchange. Certain capitalized terms used herein are
defined in paragraph 11 hereof.


In order to induce the Company and the Representative, on
behalf of the Underwriters, to enter into the Underwriting Agreement and to proceed with the Public Offering and for other good
and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, APSG Sponsor III, L.P., a Cayman Islands
limited partnership (the “Sponsor”), and each of the undersigned individuals, each of whom is a member
of the Company’s board of directors and/or management team (each, an “Insider” and, collectively,
the “Insiders”), hereby severally (and not jointly and severally) agrees with the Company as follows:


1.                 
The Sponsor and each Insider agrees that if the Company seeks shareholder approval of a proposed Business Combination (as
defined below), then in connection with such proposed Business Combination, it, he or she shall (i) vote any Shares (as defined
below) owned by it, him or her in favor of such proposed Business Combination and (ii) not redeem any Shares owned by it, him or
her in connection with such shareholder approval. If the Company seeks to consummate a proposed Business Combination by engaging
in a tender offer, the Sponsor and each Insider agrees that it, he or she will not sell or tender any Shares owned by it, him or
her to the Company in connection therewith.




    	 



    	 



    

 


2.                  
The Sponsor and each Insider hereby agrees that in the event that the Company fails to consummate a Business Combination within 21
months from the closing of the Public Offering, or up to 24 months from the closing of the Public Offering if the Company extends the period of time to consummate an initial Business Combination
(the “Completion Window”), or such later period approved by the Company’s shareholders in accordance
with the Company’s amended and restated memorandum and articles of association, the Sponsor and each Insider shall take all
reasonable steps to cause the Company to (i) cease all operations except for the purpose of winding up, (ii) as promptly as
reasonably possible but not more than ten business days thereafter, subject to lawfully available funds therefor, redeem 100% of the
Ordinary Shares sold as part of the Units in the Public Offering (the “Offering Shares”), at a per-share
price, payable in cash, equal to the aggregate amount then on deposit in the Trust Account (as defined below), including interest
earned on the funds held in the Trust Account, less amounts withdrawn to pay the Company’s taxes (“Permitted
Withdrawals”) and less up to $100,000 of interest to pay dissolution expenses, divided by the number of then
outstanding Offering Shares, which redemption will completely extinguish all Public Shareholders’ rights as shareholders
(including the right to receive further liquidating distributions, if any), subject to applicable law, and (iii) as promptly as
reasonably possible following such redemption, subject to the approval of the Company’s remaining shareholders and the
Company’s board of directors, dissolve and liquidate, subject in each case to the Company’s obligations under Cayman
Islands law to provide for claims of creditors and the requirements of other applicable law. The Sponsor and each Insider agrees to
not propose any amendment to the Company’s amended and restated memorandum and articles of association that would modify the
substance or timing of the Company’s obligation to redeem 100% of the Offering Shares if the Company does not complete a
Business Combination within the Completion Window or with respect to any other material provisions relating to shareholders’
rights or pre-initial business combination acquisition, unless the Company provides its Public Shareholders with the opportunity to
redeem their Offering Shares upon approval of any such amendment at a per-share price, payable in cash, equal to the aggregate
amount then on deposit in the Trust Account, including interest earned on the funds held in the Trust Account, less Permitted
Withdrawals, divided by the number of then outstanding Offering Shares.


The Sponsor and each Insider acknowledges that it, he or
she has no right, title, interest or claim of any kind in or to any monies held in the Trust Account as a result of any liquidation
of the Company with respect to the Founder Shares held by it, him or her. The Sponsor and each Insider hereby further waives, with
respect to any Ordinary Shares held by it, him or her, if any, any redemption rights it, he or she may have in connection with
the consummation of a Business Combination, including, without limitation, any such rights available in the context of a shareholder
vote to approve such Business Combination or in the context of a tender offer made by the Company to purchase Ordinary Shares (although
the Sponsor, the Insiders and their respective affiliates shall be entitled to redemption and liquidation rights with respect to
any Offering Shares it or they hold if the Company fails to consummate a Business Combination within the time period set forth
in the Company’s amended and restated memorandum and articles of association or 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 Offering Shares if the Company does not complete a Business Combination
within the time period set forth 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).




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3.                 
 During the period commencing on the effective date of the Underwriting Agreement and ending 180 days after such date, the
Sponsor and each Insider shall not, without the prior written consent of the Representative, (i) sell, offer to sell, contract
or agree to sell, hypothecate, pledge, grant any option to purchase or otherwise dispose of or agree to dispose of, directly or
indirectly, or establish or increase a put equivalent position or liquidate or decrease a call equivalent position within the meaning
of Section 16 of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), and the rules
and regulations of the Commission promulgated thereunder, with respect to any Units, Ordinary Shares, Founder Shares, Warrants
or any securities convertible into, or exercisable, or exchangeable for, Ordinary Shares owned by it, him or her, (ii) enter into
any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of
any Units, Ordinary Shares, Founder Shares, Warrants or any securities convertible into, or exercisable, or exchangeable for, Ordinary
Shares owned by it, him or her, whether any such transaction is to be settled by delivery of such securities, in cash or otherwise,
or (iii) publicly announce any intention to effect any transaction specified in clause (i) or (ii). Each of the Insiders and the
Sponsor acknowledges and agrees that, prior to the effective date of any release or waiver, of the restrictions set forth in this
paragraph 3 or paragraph 7 below, the Company shall announce the impending release or waiver by press release through a major news
service at least two business days before the effective date of the release or waiver. Any such release or waiver granted shall
only be effective two business days after the publication date of such press release. The provisions of this paragraph will not
apply if the release or waiver is effected solely to permit a transfer not for consideration and the transferee has agreed in writing
to be bound by the same terms described in this Letter Agreement to the extent and for the duration that such terms remain in effect
at the time of the transfer. Additionally, the provisions of this paragraph will not apply to any transfers or transactions that
are permitted under Section 7(c) of this Letter Agreement.


4.                 
In the event of the liquidation of the Trust Account, the Sponsor (which for purposes of clarification shall not extend
to any other shareholders, members or managers of the Sponsor or any other Insider) agrees to indemnify and hold harmless the Company
against any and all loss, liability, claim, damage and expense whatsoever (including, but not limited to, any and all legal or
other expenses reasonably incurred in investigating, preparing or defending against any litigation, whether pending or threatened,
or any claim whatsoever) to which the Company may become subject as a result of any claim by (i) any third party (other than the
Company’s independent accountants) for services rendered or products sold to the Company or (ii) a prospective target business
with which the Company has entered into a letter of intent, confidentiality or other similar agreement for a Business Combination
(a “Target”); provided, however, that such indemnification of the Company by the Sponsor
(x) shall apply only to the extent necessary to ensure that such claims by a third party (other than the Company’s independent
accountants) for services rendered or products sold to the Company or a Target do not reduce the amount of funds in the Trust Account
to below the lesser of (i) $10.00 per Offering Share or (ii) the actual amount per Offering Share held in the Trust Account as
of the date of the liquidation of the Trust Account, if less than $10.00 per Offering Share is then held in the Trust Account due
to reductions in the value of the trust assets less Permitted Withdrawals, (y) shall not apply to any claims by a third party (including
a Target) that executed a waiver of any and all rights to the monies held in the Trust Account (whether or not such waiver is enforceable)
and (z) shall not apply to any claims under the Company’s indemnity of the Underwriters against certain liabilities, including
liabilities under the Securities Act of 1933, as amended. The Sponsor shall have the right to defend against any such claim with
counsel of its choice reasonably satisfactory to the Company if, within 15 days following written receipt of notice of the claim
to the Sponsor, the Sponsor notifies the Company in writing that it shall undertake such defense. For the avoidance of doubt, none
of the Company’s officers or directors will indemnify the Company for claims by third parties, including, without limitation,
claims by vendors and prospective target businesses.




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5.                 
 To the extent that the Underwriters do not exercise their over-allotment option to purchase up to an additional 5,250,000
Units within 30 days from the date of the Prospectus (and as further described in the Prospectus), the Sponsor agrees that it shall
forfeit, at no cost, an aggregate number of Founder Shares equal to the product of 1,312,500 multiplied by a fraction, (i) the
numerator of which is 5,250,000 minus the number of Units purchased by the Underwriters upon the exercise of their over-allotment
option, and (ii) the denominator of which is 5,250,000. All references in this Letter Agreement to shares of the Company being
forfeited shall take effect as surrenders for no consideration of such shares as a matter of Cayman Islands law. The forfeiture
will be adjusted to the extent that the over-allotment option is not exercised in full by the Underwriters so that the Initial
Shareholders (as defined below) will own an aggregate of 20.0% of the Company’s issued and outstanding Shares after the Public
Offering. To the extent that the size of the Public Offering is increased or decreased, the Company will effect a capitalization
or share repurchase, redemption or share split or other appropriate mechanism, as applicable, immediately prior to the consummation
of the Public Offering in such amount as to maintain the ownership of the Shares of the Initial Shareholders prior to the Public
Offering at 20.0% of the Company’s issued and outstanding Shares upon the consummation of the Public Offering. In connection
with such increase or decrease in the size of the Public Offering, then (A) the references to 5,250,000 in the numerator and denominator
of the formula in the first sentence of this paragraph shall be changed to a number equal to 15% of the number of Ordinary Shares
included in the Units issued in the Public Offering and (B) the reference to 1,312,500 in the formula set forth in the immediately
preceding sentence shall be adjusted to such number of Founder Shares that the Sponsor would have to return to the Company in order
to hold (with all of the Initial Shareholders) an aggregate of 20.0% of the Company’s issued and outstanding Shares after
the Public Offering.


6.                 
The Sponsor and each Insider hereby agrees and acknowledges that: (i) the Underwriters and the Company would be irreparably
injured in the event of a breach by the Sponsor or an Insider of its, his or her obligations under paragraphs 1, 2, 3, 4, 5, 7(a)
and 7(b), as applicable, of this Letter Agreement; (ii) monetary damages may not be an adequate remedy for such breach; and (iii)
the non-breaching party shall be entitled to injunctive relief, in addition to any other remedy that such party may have in law
or in equity, in the event of such breach.


7.                  (a)
Subject to the exceptions set forth herein, the Sponsor and each Insider agrees that it, he or she shall not Transfer (as defined
below) any Founder Shares (or Ordinary Shares issuable upon conversion thereof) until the earlier of (i) one year after the
completion of the Company’s initial Business Combination, (ii) subsequent to the initial Business Combination, (x) if the last
reported sale price of the Ordinary Shares equals or exceeds $12.00 per share (as adjusted for share splits, share dividends,
reorganizations, recapitalizations and the like) for any 20 trading days within any 30-trading day period commencing at least 150
days after the Company’s initial Business Combination or (y) the date on which the Company completes a liquidation, merger,
consolidation, share exchange, reorganization or other similar transaction that results in all of the Company’s shareholders
having the right to exchange their shares for cash, securities or other property (the “Founder Shares Lock-up
Period”).


(b)              
Subject to the exceptions set forth herein, the Sponsor and each Insider agrees that it, he or she shall not Transfer any
Private Placement Warrants (as defined below) or Ordinary Shares issued or issuable upon the exercise of the Private Placement
Warrants, until 30 days after the completion of the Company’s initial Business Combination (the “Private Placement
Warrants Lock-up Period”, together with the Founder Shares Lock-up Period, the “Lock-up Periods”).




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(c)                
Notwithstanding the provisions set forth in paragraphs 3 and 7(a) and (b), Transfers of the Founder Shares, Private Placement
Warrants and Ordinary Shares issued or issuable upon the exercise or conversion of the Private Placement Warrants or the Founder
Shares and that are held by the Sponsor, any Insider or any of their permitted transferees (that have complied with this paragraph
7(c)), are permitted: (a) to the Company’s officers or directors, any affiliates or family members of any of the
Company’s officers or directors, any member of the Sponsor, or any affiliates of the Sponsor; (b) in the case of an
individual, transfers by gift to a member of one of the individual’s immediate family, to a trust, the beneficiary of which is
a member of the individual’s immediate family or an affiliate of such person, or to a charitable organization; (c) in the case
of an individual, transfers by virtue of laws of descent and distribution upon death of such person; (d) in the case of an
individual, transfers pursuant to a qualified domestic relations order; (e) transfers by virtue of the laws of the Cayman Islands or
the Sponsor’s operating agreement upon dissolution of the Sponsor; (f) transfers by private sales or transfers made in
connection with the consummation of the Company’s Business Combination at prices no greater than the price at which the
securities were originally purchased; (g) transfers in the event of the Company’s liquidation prior to the completion of the
Company’s initial Business Combination; (h) in the event of the Company’s completion of a liquidation, merger,
consolidation, share exchange, reorganization or other similar transaction which results in all of the Company’s shareholders
having the right to exchange their Ordinary Shares for cash, securities or other property subsequent to the completion of the
Company’s initial Business Combination; (i) to a nominee or custodian of a person or entity to whom a disposition or transfer
would be permissible under clauses (a) through (h) above; (j) to any third-party pledgee in a bona fide transaction as collateral to
secure obligations pursuant to lending or other arrangements between such third parties (or their affiliates or designees) and the
Sponsor, any other Insider and/or their affiliates or any similar arrangement relating to a financing arrangement for the benefit of
the Sponsor, any other Insider and/or their affiliates; and (k) pursuant to a bona fide loan or pledge or as a grant or maintenance
of a bona fide lien, security interest, pledge or other similar encumbrance (each, a “Pledge”) of any such securities
owned by the Sponsor, any other Insider and/or their affiliates to a nationally or internationally recognized financial institution
(an “Institution”) in connection with a loan to the Sponsor, such Insider and/or their affiliates; provided, however,
that (A) the Sponsor, such Insider and/or their affiliates shall not Pledge such securities resulting in a loan to value in excess
of 50%; and (B) the Sponsor, such Insider or the Company, as the case may be, shall provide Credit Suisse Securities (USA) LLC prior written notice informing them of any public filing, report or announcement made by or on behalf of the Sponsor, such Insider
or the Company with respect thereto; provided, however, that in the case of clauses (a) through (d), (f) and (i), these permitted
transferees must enter into a written agreement with the Company agreeing to be bound by the transfer restrictions herein and the
other restrictions contained in this Agreement (including provisions relating to voting, the Trust Account and liquidating
distributions).







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8.                 
The Sponsor and each Insider represents and warrants that it, he or she has never been suspended or expelled from membership
in any securities or commodities exchange or association or had a securities or commodities license or registration denied, suspended
or revoked. Each Insider’s biographical information furnished to the Company (including any such information included in
the Prospectus) is true and accurate in all respects and does not omit any material information with respect to such Insider’s
background. Each Insider’s questionnaire furnished to the Company is true and accurate in all respects. The Sponsor and each
Insider represents and warrants that: it, he or she is not subject to or a respondent in any legal action for, any injunction,
cease-and-desist order or order or stipulation to desist or refrain from any act or practice relating to the offering of securities
in any jurisdiction; it, he or she has never been convicted of, or pleaded guilty to, any crime (i) involving fraud, (ii) relating
to any financial transaction or handling of funds of another person, or (iii) pertaining to any dealings in any securities and
it, he or she is not currently a defendant in any such criminal proceeding.


 


9.                 
 [Reserved.]


10.             
The Sponsor and each Insider has full right and power, without violating any agreement to which it is bound (including,
without limitation, any non-competition or non-solicitation agreement with any employer or former employer), to enter into this
Letter Agreement and, as applicable, to serve as an officer and/or a director on the board of directors of the Company and hereby
consents to being named in the Prospectus as an officer and/or a director of the Company.


11.              As
used herein, (i) “Business Combination” shall mean a merger, consolidation, share exchange, asset
acquisition, share purchase, reorganization or similar business combination, involving the Company and one or more businesses; (ii)
 “Shares” shall mean, collectively, the Ordinary Shares and the Founder Shares; (iii) “Founder
Shares” shall mean the 9,987,500 Class B Ordinary Shares of the Company, par value $0.0001 per share (up to 1,312,500 of which are subject to complete or partial forfeiture if the over-allotment option is not exercised by the Underwriters), initially
held by the Sponsor; (iv) “Initial Shareholders” shall mean the Sponsor and any other holder of Founder
Shares immediately prior to the Public Offering; (v) “Private Placement Warrants” shall mean the warrants
to purchase 6,107,500 Ordinary Shares of the Company (or up to 6,807,500 Ordinary Shares if the Underwriters’ over-allotment
option is exercised in full) that the Sponsor has agreed to purchase for an aggregate purchase price of approximately $11.0 million
in the aggregate (or $12.2 million if the over-allotment option is exercised in full), or $1.50 per warrant, in a private placement
that shall occur simultaneously with the consummation of the Public Offering; (vi) “Public Shareholders”
shall mean the holders of securities issued in the Public Offering; (vii) “Trust Account” shall mean the
trust fund into which a portion of the net proceeds of the Public Offering and the sale of the Private Placement Warrants shall be
deposited; and (viii) “Transfer” shall mean the (a) sale or assignment of, offer to sell, contract or
agreement to sell, hypothecate, pledge, grant of any option to purchase or otherwise dispose of or agreement to dispose of, directly
or indirectly, or establishment or increase of a put equivalent position or liquidation with respect to or decrease of a call
equivalent position within the meaning of Section 16 of the Exchange Act and the rules and regulations of the Commission promulgated
thereunder with respect to, any security, (b) entry into any swap or other arrangement that transfers to another, in whole or in
part, any of the economic consequences of ownership of any security, whether any such transaction is to be settled by delivery of
such securities, in cash or otherwise, or (c) public announcement of any intention to effect any transaction specified in clause (a)
or (b).







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12.             
This Letter Agreement constitutes the entire agreement and understanding of the parties hereto in respect of the subject
matter hereof and supersedes all prior understandings, agreements, or representations by or among the parties hereto, written or
oral, to the extent they relate in any way to the subject matter hereof or the transactions contemplated hereby. This Letter Agreement
may not be changed, amended, modified or waived (other than to correct a typographical error) as to any particular provision, except
by a written instrument executed by all parties hereto.


13.             
Except as otherwise provided herein, no party hereto may assign either this Letter Agreement or any of its rights, interests,
or obligations hereunder without the prior written consent of the other parties. Any purported assignment in violation of this
paragraph shall be void and ineffectual and shall not operate to transfer or assign any interest or title to the purported assignee.
This Letter Agreement shall be binding on the Sponsor and each Insider and their respective successors, heirs and assigns and permitted
transferees.



 


14.             
 Nothing in this Letter Agreement shall be construed to confer upon, or give to, any person or entity other than the parties
hereto any right, remedy or claim under or by reason of this Letter Agreement or of any covenant, condition, stipulation, promise
or agreement hereof. All covenants, conditions, stipulations, promises and agreements contained in this Letter Agreement shall
be for the sole and exclusive benefit of the parties hereto and their successors, heirs, personal representatives and assigns and
permitted transferees.


15.             
This Letter 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.


16.             
This Letter 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 Letter 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 Letter Agreement a provision as similar in terms to such invalid or unenforceable provision as may be possible and be valid
and enforceable.


17.             
This Letter 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.
The parties hereto (i) all agree that any action, proceeding, claim or dispute arising out of, or relating in any way to, this
Letter Agreement shall be brought and enforced in the courts of New York City, in the State of New York, and irrevocably submit
to such jurisdiction and venue, which jurisdiction and venue shall be exclusive and (ii) waive any objection to such exclusive
jurisdiction and venue or that such courts represent an inconvenient forum.



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18.             
Any notice, consent or request to be given in connection with any of the terms or provisions of this Letter 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 facsimile transmission.


19.             
This Letter Agreement shall terminate on the earlier of (i) the expiration of the Lock-up Periods or (ii) the liquidation
of the Company; provided, however, that this Letter Agreement shall earlier terminate in the event that the Public
Offering is not consummated and closed by December 31, 2022; provided further that paragraph 4 of this Letter Agreement shall survive
such liquidation for a period of six (6) years.


[Signature Page follows]




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	Sincerely,
	 	 
	APSG SPONSOR III, L.P.
	 	 
	By:	 
	 	Name:
	 	Title:
	 	 
	[Insiders]
	 	 
	By:	 
	 	Name:
	 	Title:



 


 


 


Acknowledged and Agreed:


APOLLO STRATEGIC GROWTH CAPITAL III


	By:	 
	 	Name:  James Crossen
	 	Title:    Chief Financial Officer, Chief Accounting Officer and Secretary


 


 


 


 


[Signature Page to Letter Agreement]