Exhibit 4.3


[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, par value $0.0001 per share (“Ordinary
Shares”), of Apollo Strategic Growth Capital III, a Cayman Islands exempted company 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 (or through “cashless exercise” as provided for in the Warrant Agreement)
of the United States of America upon surrender of this Warrant Certificate and payment of the Warrant Price at the office or agency
of the Warrant Agent referred to below, subject to the conditions set forth herein and in the Warrant Agreement. Defined terms
used in this Warrant Certificate but not defined herein shall have the meanings given to them in the Warrant Agreement.


Each whole Warrant is initially exercisable
for one fully paid and non-assessable 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 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 each 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. The Warrants may be redeemed, subject to certain conditions,
as set forth in the Warrant Agreement.


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:
	 	Title:
	 	 
	CONTINENTAL STOCK TRANSFER & TRUST COMPANY, as Warrant
    Agent
	 
	By:	         
	 	Name:
	 	Title:
	 	 






 




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[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.




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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.




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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 subsection 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 subsection 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]




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	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).



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