Exhibit 4.1


	 	NUMBER OF UNITS
	 	 
	 	U-
	SEE REVERSE FOR CERTAIN DEFINITIONS	 
	 	CUSIP






APOLLO STRATEGIC GROWTH CAPITAL
III


UNITS CONSISTING OF ONE CLASS A
ORDINARY SHARE AND

ONE-FOURTH OF ONE REDEEMABLE WARRANT, EACH WHOLE WARRANT ENTITLING THE HOLDER TO PURCHASE ONE CLASS A ORDINARY SHARE


THIS CERTIFIES THAT                  is the owner of Units.


Each Unit (“Unit”)
consists of one (1) Class A ordinary share, par value $0.0001 per share (an “Ordinary Share”), of Apollo
Strategic Growth Capital III, a Cayman Islands exempted company incorporated with limited liability (the “Company”),
and one-fourth (1/4) of one redeemable warrant (each whole warrant exercisable for one Ordinary Share, a “Warrant”).
Each whole Warrant entitles the holder to purchase one (1) Ordinary Share (subject to adjustment) for $11.50 per share (subject
to adjustment). Only whole Warrants are exercisable. Each whole Warrant will become exercisable on the later of (i) thirty (30)
days after the Company’s completion of a merger, share exchange, asset acquisition, share purchase, reorganization or other
similar business combination with one or more businesses (each, a “Business Combination”), or (ii) twelve
(12) months from the closing of the Company’s initial public offering, and will expire unless exercised before 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,
or earlier upon redemption or liquidation (“Expiration Date”). The Ordinary Shares and Warrants comprising
the Units represented by this certificate are not transferable separately prior [___], 2021, unless [_________] elects to allow
earlier separate trading, subject to the Company’s filing of a Current Report on Form 8-K with the Securities and Exchange
Commission containing an audited balance sheet reflecting the Company’s receipt of the gross proceeds of the Company’s
initial public offering and issuing a press release announcing when separate trading will begin. No fractional Warrants will be
issued upon separation of the Units and only whole Warrants will trade. The terms of the Warrants are governed by a Warrant Agreement,
dated as of [___], 2021, between the Company and Continental Stock Transfer & Trust Company, as Warrant Agent, and are subject
to the terms and provisions contained therein, all of which terms and provisions the holder of this certificate consents to by
acceptance hereof. Copies of the Warrant Agreement are on file at the office of the Warrant Agent at One State Street, 30th
Floor, New York, New York 10014, and are available to any Warrant holder on written request and without cost.




    	 



    	 



    

Upon the consummation of the Company’s
initial Business Combination, the Units represented by this certificate will automatically separate into the Ordinary Shares and
Warrants comprising such Units.


This certificate is not valid unless countersigned
by the Transfer Agent and registered by the Registrar of the Company.


This certificate shall be governed by and
construed in accordance with the internal laws of the State of New York.


Witness the facsimile signature of its
duly authorized officers.


	 	 	 
	Secretary	 	Chief Executive Officer



 



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Apollo Strategic Growth Capital
III


The Company will furnish without charge
to each unitholder who so requests, a statement of the powers, designations, preferences and relative, participating, optional
or other special rights of each class of shares or series thereof of the Company and the qualifications, limitations, or restrictions
of such preferences and/or rights.


The following abbreviations, when used
in the inscription on the face of this certificate, shall be construed as though they were written out in full according to applicable
laws or regulations:





	TEN COM	–	as tenants in common	UNIF GIFT MIN

 ACT	–  	 	Custodian 	 
	TEN ENT	–	as tenants by the entireties	 	 	(Cust)	 	(Minor)
	JT TEN	–	as joint tenants with right of survivorship and not as tenants in common	 	 	under Uniform Gifts to Minors Act
	 	 	 	 	 	 	(State)	 
	 	 	 	 	 	 	 	 



 Additional abbreviations may also
be used though not in the above list.


For value received, hereby sell, assign and transfer unto


PLEASE INSERT SOCIAL SECURITY OR


OTHER


IDENTIFYING NUMBER OF ASSIGNEE





	(PLEASE PRINT OR TYPEWRITE NAME AND ADDRESS,
INCLUDING ZIP

CODE, OF ASSIGNEE)
	 
	 
	 
	 
	 
	 


Units represented by the within Certificate, and do hereby irrevocably
constitute and appoint Attorney to transfer the said Units on the books of the within named Company with full power of substitution
in the premises.


	 	 	 	 	 
	Dated:	 	 	 	 
	 	 	 	Notice:	The signature to this assignment must correspond with the name as written upon the face of the certificate in every particular, without alteration or enlargement or any change whatever.


 




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	Signature(s) Guaranteed:
	 
	THE SIGNATURE(S) MUST BE GUARANTEED BY AN ELIGIBLE GUARANTOR INSTITUTION (BANKS, STOCKBROKERS, SAVINGS AND LOAN ASSOCIATIONS AND CREDIT UNIONS WITH MEMBERSHIP IN AN APPROVED SIGNATURE GUARANTEE MEDALLION PROGRAM, PURSUANT TO S.E.C. RULE 17Ad-15 (OR ANY SUCCESSOR RULE)).



 



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In each case, as more fully described in
the Company’s final prospectus dated [___], 2021, the holder(s) of the Company’s Class A ordinary shares shall be entitled
to receive a pro-rata portion of certain funds held in the trust account established in connection with the Company’s initial
public offering only in the event that (i) the Company redeems the Class A ordinary shares sold in its initial public offering
and liquidates because it does not consummate an initial business combination by [___], 2023 (or such later date if such period
is extended pursuant to the Company’s amended and restated memorandum and articles of association as in effect at such time),
(ii) the Company redeems the Class A ordinary shares sold in its initial public offering 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 the Class A ordinary shares if it does not consummate an
initial business combination by [___], 2023 (or such later date if such period is extended pursuant to the Company’s amended
and restated memorandum and articles of association as in effect at such time) or with respect to any other material provisions
relating to shareholders’ rights or pre-initial business combination activity, or (iii) if the holder(s) seek(s) to redeem
for cash his, her or its respective Class A ordinary shares in connection with a tender offer (or proxy solicitation, solely in
the event the Company seeks shareholder approval of the proposed initial business combination) setting forth the details of a proposed
initial business combination. In no other circumstances shall the holder(s) have any right or interest of any kind in or to the
trust account.



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