Exhibit 10.4


FORM OF REGISTRATION RIGHTS AGREEMENT


THIS REGISTRATION RIGHTS AGREEMENT (this
 “Agreement”), dated as of [___], 2021, is made and entered into by and among Apollo Strategic Growth
Capital III, a Cayman Islands exempted company, incorporated with limited liability (the “Company”),
APSG Sponsor III, L.P., a Cayman Islands exempted limited partnership (the “Sponsor”), and the undersigned
parties listed under Holder on the signature pages hereto (each such party, together with the Sponsor and any person or entity
who hereafter becomes a party to this Agreement pursuant to Section 5.2 of this Agreement, a “Holder”
and collectively the “Holders”).


RECITALS


WHEREAS, the Sponsor and the Company’s
initial shareholders own an aggregate of 11,500,000 Class B ordinary shares, par value $0.0001 per share, of the Company (the “Founder
Shares”), up to 1,500,000 of which are subject to forfeiture to the Company for no consideration depending on the
extent to which the underwriters of the Company’s initial public offering exercise their over-allotment option;


WHEREAS, the Founder Shares will
automatically convert into Class A ordinary shares, par value $0.0001 per share, of the Company (the “Ordinary Shares”)
at the time of the Company’s initial business combination on a one-for-one basis, subject to adjustment, on the terms and
conditions provided in the Company’s amended and restated memorandum and articles of association;


WHEREAS, on [___], 2021, the Company
and the Sponsor entered into that certain Private Placement Warrants Purchase Agreement (the “Private Placement Warrants
Purchase Agreement”), pursuant to which the Sponsor agreed to purchase 7,333,333 warrants (or up to 8,133,333 warrants
if the over-allotment option in connection with the Company’s initial public offering is exercised in full) (the “Private
Placement Warrants”), in a private placement transaction occurring simultaneously with the closing of the Company’s
initial public offering (and the closing over the over-allotment option, if applicable); and


WHEREAS, in order to finance the Company’s
transaction costs in connection with its search for and consummation of an initial Business Combination (as defined below) the
Sponsor or affiliates of the Sponsor or certain of the Company’s officers and directors may loan to the Company funds as
the Company may require, of which up to $2,000,000 of such loans may be convertible into warrants (“Working Capital
Warrants”) at a price of $1.50 per warrant; and


WHEREAS, the Company and the Holders
desire to enter into this Agreement, pursuant to which the Company shall grant the Holders certain registration rights with respect
to certain securities of the Company, as set forth in this Agreement.


NOW, THEREFORE, in
consideration of the representations, covenants and agreements contained herein, and certain other good and valuable
consideration, the receipt and sufficiency of which are hereby acknowledged,
the parties hereto, intending to be legally bound, hereby agree as follows:




    


     


    




ARTICLE I

DEFINITIONS


1.1.           
Definitions. The terms defined in this Article I shall, for all purposes of this Agreement, have the respective
meanings set forth below:


“Adverse Disclosure”
shall mean any public disclosure of material non-public information, which disclosure, in the good faith judgment of the Chief
Executive Officer or principal financial officer of the Company, after consultation with counsel to the Company, (i) would be required
to be made in any Registration Statement or Prospectus in order for the applicable Registration Statement or Prospectus not to
contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements contained therein
(in the case of any prospectus and any preliminary prospectus, in the light of the circumstances under which they were made) not
misleading, (ii) would not be required to be made at such time if the Registration Statement were not being filed, and (iii) the
Company has a bona fide business purpose for not making such information public.


“Agreement” shall
have the meaning given in the Preamble.


“Board” shall
mean the Board of Directors of the Company.


“Business Combination”
shall mean any merger, share exchange, asset acquisition, share purchase, reorganization or other similar business combination
with one or more businesses, involving the Company.


“Commission”
shall mean the Securities and Exchange Commission.


“Company” shall
have the meaning given in the Preamble.


“Demand Registration”
shall have the meaning given in subsection 2.1.1.


“Demanding Holder”
shall have the meaning given in subsection 2.1.1.


“Exchange Act”
shall mean the Securities Exchange Act of 1934, as it may be amended from time to time.


“Form S-1” shall
have the meaning given in subsection 2.1.1.


“Form S-3” shall
have the meaning given in subsection 2.3.


“Founder Shares”
shall have the meaning given in the Recitals hereto and shall be deemed to include the Ordinary Shares issuable upon conversion
thereof.




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“Founder Shares Lock-up Period”
shall mean, with respect to the Founder Shares, the period ending on the earlier of (A) one year after the date of the consummation
of the Company’s initial Business Combination or (B) subsequent to the Company’s initial Business Combination, (i)
the date on which the last 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 consummation of the Company’s initial Business Combination or (ii) the date on which the Company
consummates a liquidation, merger, 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.


“Holders” shall
have the meaning given in the Preamble.


“Insider Letter”
shall mean that certain letter agreement, dated as of [___], 2021, by and among the Company, the Sponsor and each of the Company’s
officers, directors and director nominees.


“Maximum Number of Securities”
shall have the meaning given in subsection 2.1.4.


“Misstatement”
shall mean an untrue statement of a material fact or an omission to state a material fact required to be stated in a Registration
Statement or Prospectus, or necessary to make the statements in a Registration Statement or Prospectus (in the case of a Prospectus,
in the light of the circumstances under which they were made) not misleading.


“Ordinary Shares”
shall have the meaning given in the Recitals hereto.


“Permitted Transferees”
shall mean any person or entity to whom a Holder of Registrable Securities is permitted to transfer such Registrable Securities
prior to the expiration of the Founder Shares Lock-up Period, Private Placement Lock-up Period or any other lock-up period, as
the case may be, and pursuant to the Insider Letter, the Private Placement Warrants Purchase Agreement, this Agreement and any
other applicable agreement between such Holder and the Company, in each case for so long as such agreements remain in effect, and
to any transferee thereafter.


“Piggyback Registration”
shall have the meaning given in subsection 2.2.1.


“Private Placement Lock-up
Period” shall mean, with respect to Private Placement Warrants that are held by the initial purchasers of such Private
Placement Warrants or their Permitted Transferees, and any Ordinary Shares issued or issuable upon the exercise or conversion of
the Private Placement Warrants that are held by the initial purchasers of the Private Placement Warrants or their Permitted Transferees,
the period ending 30 days after the completion of the Company’s initial Business Combination.




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“Private Placement Warrants”
shall have the meaning given in the Recitals hereto.


“Private Placement Warrants
Purchase Agreement” shall have the meaning given in the Recitals hereto.


“Prospectus”
shall mean the prospectus included in any Registration Statement, as supplemented by any and all prospectus supplements and as
amended by any and all post-effective amendments and including all material incorporated by reference in such prospectus.


“Prospectus Date”
shall mean the date of the final prospectus filed with the Commission and relating to the Company’s initial public offering.


“Registrable Security”
shall mean (a) the Founder Shares and the Ordinary Shares issued or issuable upon the conversion of any Founder Shares, (b) the
Private Placement Warrants (including any Ordinary Shares issued or issuable upon the exercise of any such Private Placement Warrants),
(c) any outstanding Ordinary Shares or any other equity security (including, without limitation, Ordinary Shares issued or issuable
upon the exercise of any other equity security, units comprising Ordinary Shares and warrants, or warrants) of the Company held
by a Holder from time to time, (d) any equity securities (including Ordinary Shares issued or issuable upon the exercise of any
such equity security) of the Company issuable upon conversion of any working capital loans in an amount of up to $2,000,000 made
to the Company by a Holder (including the Working Capital Warrants and any Ordinary Shares issuable upon the exercise of the Working
Capital Warrants) and (e) any other equity security of the Company issued or issuable with respect to any such Ordinary Share by
way of a share dividend or share split or in connection with a combination of shares, recapitalization, merger, consolidation or
reorganization; provided, however, that, as to any particular Registrable Security, such securities shall cease to
be Registrable Securities when: (A) a Registration Statement with respect to the sale of such securities shall have become effective
under the Securities Act and such securities shall have been sold, transferred, disposed of or exchanged in accordance with such
Registration Statement; (B) such securities shall have been otherwise transferred, new certificates for such securities not bearing
a legend restricting further transfer shall have been delivered by the Company and subsequent public distribution of such securities
shall not require registration under the Securities Act; (C) such securities shall have ceased to be outstanding; (D) such securities
may be sold without registration pursuant to Rule 144 promulgated under the Securities Act (or any successor rule promulgated thereafter
by the Commission) (but with no volume or other restrictions or limitations); or (E) such securities have been sold to, or through,
a broker, dealer or underwriter in a public distribution or other public securities transaction.


“Registration”
shall mean a registration effected by preparing and filing a registration statement or similar document in compliance with the
requirements of the Securities Act, and the applicable rules and regulations promulgated thereunder, and such registration statement
becoming effective.




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“Registration Expenses”
shall mean the out-of-pocket expenses of a Registration, including, without limitation, the following:


(A)            
all registration and filing fees (including fees with respect to filings required to be made with the Financial Industry
Regulatory Authority, Inc.) and any securities exchange on which the Ordinary Shares are then listed;


(B)             
fees and expenses of compliance with securities or blue sky laws (including reasonable fees and disbursements of counsel
for the Underwriters in connection with blue sky qualifications of Registrable Securities);


(C)             
printing, messenger, telephone and delivery expenses;


(D)            
reasonable fees and disbursements of counsel for the Company;


(E)             
reasonable fees and disbursements of all independent registered public accountants of the Company incurred specifically
in connection with such Registration; and


(F)              
reasonable fees and expenses of one (1) legal counsel selected by the majority-in-interest of the Demanding Holders initiating
a Demand Registration to be registered for offer and sale in the applicable Registration.


“Registration Statement”
shall mean any registration statement that covers the Registrable Securities pursuant to the provisions of this Agreement, including
the Prospectus included in such registration statement, amendments (including post-effective amendments) and supplements to such
registration statement, and all exhibits to and all material incorporated by reference in such registration statement.


“Requesting Holder”
shall have the meaning given in subsection 2.1.1.


“Securities Act”
shall mean the Securities Act of 1933, as amended from time to time.


“Sponsor” shall
have the meaning given in the Preamble hereto.


“Underwriter”
shall mean a securities dealer who purchases any Registrable Securities as principal in an Underwritten Offering and not as part
of such dealer’s market-making activities.


“Underwritten Registration”
or “Underwritten Offering” shall mean a Registration in which securities of the Company are sold to an
Underwriter in a firm commitment underwriting for distribution to the public.


“Working Capital Warrants”
shall have the meaning given in the Recitals hereto.






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    ARTICLE II

REGISTRATIONS


2.1.           
Demand Registration.


2.1.1       
Request for Registration. Subject to the provisions of subsection 2.1.4 and Section 2.4 hereof, at
any time and from time to time on or after the date the Company consummates the Business Combination, the Holders of at least fifteen
percent (15%) of the then-outstanding number of Registrable Securities (the “Demanding Holders”) may
make a written demand for Registration of all or part of their Registrable Securities, which written demand shall describe the
amount and type of securities to be included in such Registration and the intended method(s) of distribution thereof (such written
demand a “Demand Registration”). The Company shall, within ten (10) days of the Company’s receipt
of the Demand Registration, notify, in writing, all other Holders of Registrable Securities of such demand, and each Holder of
Registrable Securities who thereafter wishes to include all or a portion of such Holder’s Registrable Securities in a Registration
pursuant to a Demand Registration (each such Holder that includes all or a portion of such Holder’s Registrable Securities
in such Registration, a “Requesting Holder”) shall so notify the Company, in writing, within five (5)
days after the receipt by the Holder of the notice from the Company. Upon receipt by the Company of any such written notification
from a Requesting Holder(s) to the Company, such Requesting Holder(s) shall be entitled to have their Registrable Securities included
in a Registration pursuant to a Demand Registration and the Company shall effect, as soon thereafter as practicable, but not more
than forty five (45) days immediately after the Company’s receipt of the Demand Registration, the Registration of all Registrable
Securities requested by the Demanding Holders and Requesting Holders pursuant to such Demand Registration. Under no circumstances
shall the Company be obligated to effect more than an aggregate of three (3) Registrations pursuant to a Demand Registration under
this subsection 2.1.1 with respect to any or all Registrable Securities; provided, however, that a Registration
shall not be counted for such purposes unless a Form S-1 or any similar long-form registration statement that may be available
at such time (“Form S-1”) has become effective and all of the Registrable Securities requested by the
Requesting Holders to be registered on behalf of the Requesting Holders in such Form S-1 Registration have been sold, in accordance
with Section 3.1 of this Agreement. Notwithstanding the foregoing, APSG Sponsor III, L.P. may not exercise its demand registration
rights after five (5) years from the pricing date of the Company’s initial public offering and may not exercise its demand
rights on more than one occasion.


2.1.2       
Effective Registration. Notwithstanding the provisions of subsection 2.1.1 above or any other part of this
Agreement, a Registration pursuant to a Demand Registration shall not count as a Registration unless and until (i) the Registration
Statement filed with the Commission with respect to a Registration pursuant to a Demand Registration has been declared effective
by the Commission and (ii) the Company has complied with all of its obligations under this Agreement with respect thereto; provided,
further, that if, after such Registration Statement has been declared effective, an offering of Registrable Securities in
a Registration pursuant to a Demand Registration is subsequently interfered with by any stop order or injunction of the Commission,
federal or state court or any other governmental agency the Registration
Statement with respect to such Registration shall be deemed not to have been declared effective, unless and until, (i) such stop
order or injunction is removed, rescinded or otherwise terminated, and (ii) a majority-in-interest of the Demanding Holders initiating
such Demand Registration thereafter affirmatively elect to continue with such Registration and accordingly notify the Company in
writing, but in no event later than five (5) days, of such election; and provided, further, that the Company shall
not be obligated or required to file another Registration Statement until the Registration Statement that has been previously filed
with respect to a Registration pursuant to a Demand Registration becomes effective or is subsequently terminated.




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2.1.3       
Underwritten Offering. Subject to the provisions of subsection 2.1.4 and Section 2.4 hereof, if a majority-in-interest
of the Demanding Holders so advise the Company as part of their Demand Registration that the offering of the Registrable Securities
pursuant to such Demand Registration shall be in the form of an Underwritten Offering, then the right of such Demanding Holder
or Requesting Holder (if any) to include its Registrable Securities in such Registration shall be conditioned upon such Holder’s
participation in such Underwritten Offering and the inclusion of such Holder’s Registrable Securities in such Underwritten
Offering to the extent provided herein. All such Holders proposing to distribute their Registrable Securities through an Underwritten
Offering under this subsection 2.1.3 shall enter into an underwriting agreement in customary form with the Underwriter(s)
selected for such Underwritten Offering by the majority-in-interest of the Demanding Holders initiating the Demand Registration.


2.1.4       
Reduction of Underwritten Offering. If the managing Underwriter or Underwriters in an Underwritten Registration pursuant
to a Demand Registration, in good faith, advises the Company, the Demanding Holders and the Requesting Holders (if any) in writing
that the dollar amount or number of Registrable Securities that the Demanding Holders and the Requesting Holders (if any) desire
to sell, taken together with all other Ordinary Shares or other equity securities that the Company desires to sell and Ordinary
Shares, if any, as to which a Registration has been requested pursuant to separate written contractual piggy-back registration
rights held by any other shareholders who desire to sell, exceeds the maximum dollar amount or maximum number of equity securities
that can be sold in the Underwritten Offering without adversely affecting the proposed offering price, the timing, the distribution
method, or the probability of success of such offering (such maximum dollar amount or maximum number of such securities, as applicable,
the “Maximum Number of Securities”), then the Company shall include in such Underwritten Offering, as
follows: (i) first, the Registrable Securities of the Demanding Holders and the Requesting Holders (if any) (pro rata based on
the respective number of Registrable Securities that each Demanding Holder and Requesting Holder (if any) has requested be included
in such Underwritten Registration and the aggregate number of Registrable Securities that the Demanding Holders and Requesting
Holders have requested be included in such Underwritten Registration) that can be sold without exceeding the Maximum Number of
Securities; (ii) second, to the extent that the Maximum Number of Securities has not been reached under the foregoing clause
(i), the Registrable Securities of Holders exercising their rights to register their Registrable Securities pursuant to subsection
2.2.1 hereof (pro rata based on the respective number of Registrable Securities that each Holder has so requested),
without exceeding the Maximum Number of Securities; (iii) third, to the extent that the Maximum Number of Securities has not been
reached under the foregoing clauses (i) and (ii), Ordinary Shares or other equity securities that the Company desires
to sell, which can be sold without exceeding the Maximum Number of Securities; and (iv) fourth, to the extent that the Maximum
Number of Securities has not been reached under the foregoing clauses (i), (ii) and (iii), Ordinary Shares
or other equity securities of other persons or entities that the Company is obligated to register in a Registration pursuant to
separate written contractual arrangements with such persons and that can be sold without exceeding the Maximum Number of Securities.




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2.1.5       
Demand Registration Withdrawal. A majority-in-interest of the Demanding Holders initiating a Demand Registration
or a majority-in-interest of the Requesting Holders (if any), pursuant to a Registration under subsection 2.1.1 shall have
the right to withdraw from a Registration pursuant to such Demand Registration for any or no reason whatsoever upon written notification
to the Company and the Underwriter or Underwriters (if any) of their intention to withdraw from such Registration prior to the
effectiveness of the Registration Statement filed with the Commission with respect to the Registration of their Registrable Securities
pursuant to such Demand Registration. Notwithstanding anything to the contrary in this Agreement, the Company shall be responsible
for the Registration Expenses incurred in connection with a Registration pursuant to a Demand Registration prior to its withdrawal
under this subsection 2.1.5.


2.2.           
Piggyback Registration.


2.2.1       
Piggyback Rights. If, at any time on or after the date the Company consummates a Business Combination, the Company
proposes to file a Registration Statement under the Securities Act with respect to an offering of equity securities, or securities
or other obligations exercisable or exchangeable for, or convertible into equity securities, for its own account or for the account
of shareholders of the Company (or by the Company and by the shareholders of the Company including, without limitation, pursuant
to Section 2.1 hereof), other than a Registration Statement (i) filed in connection with any employee share option or other
benefit plan, (ii) for an exchange offer or offering of securities solely to the Company’s existing shareholders, (iii) for
an offering of debt that is convertible into equity securities of the Company or (iv) for a dividend reinvestment plan, then the
Company shall give written notice of such proposed filing to all of the Holders of Registrable Securities as soon as practicable
but not less than ten (10) days before the anticipated filing date of such Registration Statement, which notice shall (A) describe
the amount and type of securities to be included in such offering, the intended method(s) of distribution, and the name of the
proposed managing Underwriter or Underwriters, if any, in such offering, and (B) offer to all of the Holders of Registrable Securities
the opportunity to register the sale of such number of Registrable Securities as such Holders may request in writing within five
(5) days after receipt of such written notice (such Registration a “Piggyback Registration”). The Company
shall, in good faith, cause such Registrable Securities to be included in such Piggyback Registration and shall use its best efforts
to cause the managing Underwriter or Underwriters of a proposed Underwritten Offering to permit the Registrable Securities requested
by the Holders pursuant to this subsection 2.2.1 to be included in
a Piggyback Registration on the same terms and conditions as any similar securities of the Company included in such Registration
and to permit the sale or other disposition of such Registrable Securities in accordance with the intended method(s) of distribution
thereof. All such Holders proposing to distribute their Registrable Securities through an Underwritten Offering under this subsection
2.2.1 shall enter into an underwriting agreement in customary form with the Underwriter(s) selected for such Underwritten Offering
by the Company. Notwithstanding the foregoing, APSG Sponsor III, L.P. may not exercise its “piggyback” registration
rights after seven (7) years from the pricing date of the Company’s initial public offering.




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2.2.2       
Reduction of Piggyback Registration. If the managing Underwriter or Underwriters in an Underwritten Registration
that is to be a Piggyback Registration, in good faith, advises the Company and the Holders of Registrable Securities participating
in the Piggyback Registration in writing that the dollar amount or number of Ordinary Shares that the Company desires to sell,
taken together with (i) the Ordinary Shares, if any, as to which Registration has been demanded pursuant to separate written contractual
arrangements with persons or entities other than the Holders of Registrable Securities hereunder, (ii) the Registrable Securities
as to which registration has been requested pursuant to Section 2.2 hereof, and (iii) the Ordinary Shares, if any, as to
which Registration has been requested pursuant to separate written contractual piggy-back registration rights of other shareholders
of the Company, exceeds the Maximum Number of Securities, then:


(a)               
If the Registration is undertaken for the Company’s account, the Company shall include in any such Registration (A)
first, the Ordinary Shares or other equity securities that the Company desires to sell, which can be sold without exceeding the
Maximum Number of Securities; (B) second, to the extent that the Maximum Number of Securities has not been reached under the foregoing
clause (A), the Registrable Securities of Holders exercising their rights to register their Registrable Securities pursuant
to subsection 2.2.1 hereof (pro rata based on the number of Registrable Securities that each Holder has so requested), which
can be sold without exceeding the Maximum Number of Securities; and (C) third, to the extent that the Maximum Number of Securities
has not been reached under the foregoing clauses (A) and (B), Ordinary Shares, if any, as to which Registration has
been requested pursuant to written contractual piggy-back registration rights of other shareholders of the Company, which can be
sold without exceeding the Maximum Number of Securities;


(b)              
If the Registration is pursuant to a request by persons or entities other than the Holders of Registrable Securities, then
the Company shall include in any such Registration (A) first, Ordinary Shares or other equity securities, if any, of such requesting
persons or entities, other than the Holders of Registrable Securities, which can be sold without exceeding the Maximum Number of
Securities; (B) second, to the extent that the Maximum Number of Securities has not been reached under the foregoing clause
(A), the Registrable Securities of Holders exercising their rights to register their Registrable Securities pursuant to subsection
2.2.1 hereof, (pro rata based on the number of Registrable Securities that each Holder has so requested), which can be sold
without exceeding the Maximum Number of Securities; (C) third, to
the extent that the Maximum Number of Securities has not been reached under the foregoing clauses (A) and (B), Ordinary
Shares or other equity securities that the Company desires to sell, which can be sold without exceeding the Maximum Number of Securities;
and (D) fourth, to the extent that the Maximum Number of Securities has not been reached under the foregoing clauses (A),
(B) and (C), Ordinary Shares or other equity securities for the account of other persons or entities that the Company
is obligated to register pursuant to separate written contractual arrangements with such persons or entities, which can be sold
without exceeding the Maximum Number of Securities.




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2.2.3       
Piggyback Registration Withdrawal. Any Holder of Registrable Securities shall have the right to withdraw from a Piggyback
Registration for any or no reason whatsoever upon written notification to the Company and the Underwriter or Underwriters (if any)
of his, her or its intention to withdraw from such Piggyback Registration prior to the effectiveness of the Registration Statement
filed with the Commission with respect to such Piggyback Registration. The Company (whether on its own good faith determination
or as the result of a request for withdrawal by persons pursuant to separate written contractual obligations) may withdraw a Registration
Statement filed with the Commission in connection with a Piggyback Registration at any time prior to the effectiveness of such
Registration Statement. Notwithstanding anything to the contrary in this Agreement, the Company shall be responsible for the Registration
Expenses incurred in connection with the Piggyback Registration prior to its withdrawal under this subsection 2.2.3.


2.2.4       
Unlimited Piggyback Registration Rights. For purposes of clarity, any Registration effected pursuant to Section
2.2 hereof shall not be counted as a Registration pursuant to a Demand Registration effected under Section 2.1 hereof.


2.3.           
Registrations on Form S-3. The Holders of Registrable Securities may at any time, and from time to time, request
in writing that the Company, pursuant to Rule 415 under the Securities Act (or any successor rule promulgated thereafter by the
Commission), register the resale of any or all of their Registrable Securities on Form S-3 or any similar short-form registration
statement that may be available at such time (“Form S-3”); provided, however, that the
Company shall not be obligated to effect such request through an Underwritten Offering. Within five (5) days of the Company’s
receipt of a written request from a Holder or Holders of Registrable Securities for a Registration on Form S-3, the Company shall
promptly give written notice of the proposed Registration on Form S-3 to all other Holders of Registrable Securities, and each
Holder of Registrable Securities who thereafter wishes to include all or a portion of such Holder’s Registrable Securities
in such Registration on Form S-3 shall so notify the Company, in writing, within ten (10) days after the receipt by the Holder
of the notice from the Company. As soon as practicable thereafter, but not more than twelve (12) days after the Company’s
initial receipt of such written request for a Registration on Form S-3, the Company shall register all or such portion of such
Holder’s Registrable Securities as are specified in such written request, together with all or such portion of Registrable
Securities of any other Holder or Holders joining in such request as are specified in the written notification given by such Holder
or Holders; provided, however, that the Company shall not be obligated to effect any such Registration
pursuant to Section 2.3 hereof if (i) a Form S-3 is not available for such offering; or (ii) the Holders of Registrable
Securities, together with the Holders of any other equity securities of the Company entitled to inclusion in such Registration,
propose to sell the Registrable Securities and such other equity securities (if any) at any aggregate price to the public of less
than $25,000,000. Any request for any underwritten offering pursuant to a Form S-3 shall follow the procedures of Section 2.1
(including Section 2.1.4) but, for the avoidance of doubt, shall not count as a demand registration or an exercise of any
demand rights.




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2.4.           
Restrictions on Registration Rights. If (A) during the period starting with the date sixty (60) days prior to the
Company’s good faith estimate of the date of the filing of, and ending on a date one hundred and twenty (120) days after
the effective date of, a Company initiated Registration and provided that the Company has delivered written notice to the
Holders prior to receipt of a Demand Registration pursuant to subsection 2.1.1 and it continues to actively employ, in good
faith, all reasonable efforts to cause the applicable Registration Statement to become effective; (B) the Holders have requested
an Underwritten Registration and the Company and the Holders are unable to obtain the commitment of underwriters to firmly underwrite
the offer; or (C) in the good faith judgment of the Board such Registration would be seriously detrimental to the Company and the
Board concludes as a result that it is essential to defer the filing of such Registration Statement at such time, then in each
case the Company shall furnish to such Holders a certificate signed by the Chairman of the Board stating that in the good faith
judgment of the Board it would be seriously detrimental to the Company for such Registration Statement to be filed in the near
future and that it is therefore essential to defer the filing of such Registration Statement. In such event, the Company shall
have the right to defer such filing for a period of not more than thirty (30) days; provided, however, that the Company
shall not defer its obligation in this manner more than once in any 12-month period. Notwithstanding anything to the contrary contained
in this Agreement, no Registration shall be effected or permitted and no Registration Statement shall become effective, with respect
to any Registrable Securities held by any Holder, until after the expiration of the Founder Shares Lock-up Period or the Private
Placement Lock-up Period, as the case may be.


ARTICLE III

COMPANY PROCEDURES


3.1.           
General Procedures. If at any time on or after the date the Company consummates a Business Combination the Company
is required to effect the Registration of Registrable Securities, the Company shall use its best efforts to effect such Registration
to permit the sale of such Registrable Securities in accordance with the intended plan of distribution thereof, and pursuant thereto
the Company shall, as expeditiously as possible:


3.1.1       
prepare and file with the Commission as soon as practicable a Registration Statement with respect to such Registrable Securities
and use its reasonable best efforts to cause such Registration Statement to become effective and remain effective until all Registrable Securities covered by such
Registration Statement have been sold;




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3.1.2       
 prepare and file with the Commission such amendments and post-effective amendments to the Registration Statement, and such
supplements to the Prospectus, as may be requested by the Holders or any Underwriter of Registrable Securities or as may be required
by the rules, regulations or instructions applicable to the registration form used by the Company or by the Securities Act or rules
and regulations thereunder to keep the Registration Statement effective until all Registrable Securities covered by such Registration
Statement are sold in accordance with the intended plan of distribution set forth in such Registration Statement or supplement
to the Prospectus;


3.1.3       
prior to filing a Registration Statement or prospectus, or any amendment or supplement thereto, furnish without charge to
the Underwriters, if any, and the Holders of Registrable Securities included in such Registration, and such Holders’ legal
counsel, copies of such Registration Statement as proposed to be filed, each amendment and supplement to such Registration Statement
(in each case including all exhibits thereto and documents incorporated by reference therein), the Prospectus included in such
Registration Statement (including each preliminary Prospectus), and such other documents as the Underwriters and the Holders of
Registrable Securities included in such Registration or the legal counsel for any such Holders may request in order to facilitate
the disposition of the Registrable Securities owned by such Holders;


3.1.4       
prior to any public offering of Registrable Securities, use its best efforts to (i) register or qualify the Registrable
Securities covered by the Registration Statement under such securities or “blue sky” laws of such jurisdictions
in the United States as the Holders of Registrable Securities included in such Registration Statement (in light of their intended
plan of distribution) may request and (ii) take such action necessary to cause such Registrable Securities covered by the Registration
Statement to be registered with or approved by such other governmental authorities as may be necessary by virtue of the business
and operations of the Company and do any and all other acts and things that may be necessary or advisable to enable the Holders
of Registrable Securities included in such Registration Statement to consummate the disposition of such Registrable Securities
in such jurisdictions; provided, however, that the Company shall not be required to qualify generally to do business
in any jurisdiction where it would not otherwise be required to qualify or take any action to which it would be subject to general
service of process or taxation in any such jurisdiction where it is not then otherwise so subject;


3.1.5       
cause all such Registrable Securities to be listed on each securities exchange or automated quotation system on which similar
securities issued by the Company are then listed;


3.1.6       
provide a transfer agent or warrant agent, as applicable, and registrar for all such Registrable Securities no later than
the effective date of such Registration Statement;




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3.1.7       
 advise each seller of such Registrable Securities, promptly after it shall receive notice or obtain knowledge thereof,
of the issuance of any stop order by the Commission suspending the effectiveness of such Registration Statement or the initiation
or threatening of any proceeding for such purpose and promptly use its reasonable best efforts to prevent the issuance of any stop
order or to obtain its withdrawal if such stop order should be issued;


3.1.8       
at least five (5) days prior to the filing of any Registration Statement or Prospectus or any amendment or supplement to
such Registration Statement or Prospectus or any document that is to be incorporated by reference into such Registration Statement
or Prospectus, furnish a copy thereof to each seller of such Registrable Securities or its counsel;


3.1.9       
notify the Holders at any time when a Prospectus relating to such Registration Statement is required to be delivered under
the Securities Act, of the happening of any event as a result of which the Prospectus included in such Registration Statement,
as then in effect, includes a Misstatement, and then to correct such Misstatement as set forth in Section 3.4 hereof;


3.1.10   
permit a representative of the Holders, the Underwriters, if any, and any attorney or accountant retained by such Holders
or Underwriter to participate, at each such person’s own expense, in the preparation of the Registration Statement, and cause
the Company’s officers, directors and employees to supply all information reasonably requested by any such representative,
Underwriter, attorney or accountant in connection with the Registration; provided, however, that such representatives
or Underwriters enter into a confidentiality agreement, in form and substance reasonably satisfactory to the Company, prior to
the release or disclosure of any such information;


3.1.11   
obtain a “cold comfort” letter from the Company’s independent registered public accountants in the event
of an Underwritten Registration, in customary form and covering such matters of the type customarily covered by “cold comfort”
letters as the managing Underwriter may reasonably request, and reasonably satisfactory to a majority-in-interest of the participating
Holders;


3.1.12   
on the date the Registrable Securities are delivered for sale pursuant to such Registration, obtain an opinion, dated such
date, of counsel representing the Company for the purposes of such Registration, addressed to the Holders, the placement agent
or sales agent, if any, and the Underwriters, if any, covering such legal matters with respect to the Registration in respect of
which such opinion is being given as the Holders, placement agent, sales agent, or Underwriter may reasonably request and as are
customarily included in such opinions and negative assurance letters, and reasonably satisfactory to a majority in interest of
the participating Holders;


3.1.13   
in the event of any Underwritten Offering, enter into and perform its obligations under an underwriting agreement, in usual
and customary form, with the managing Underwriter of such offering;




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3.1.14   
 make available to its security holders, as soon as reasonably practicable, an earnings statement covering the period of
at least twelve (12) months beginning with the first day of the Company’s first full calendar quarter after the effective
date of the Registration Statement which satisfies the provisions of Section 11(a) of the Securities Act and Rule 158 thereunder
(or any successor rule promulgated thereafter by the Commission);


3.1.15   
if the Registration involves the Registration of Registrable Securities involving gross proceeds in excess of $25,000,000,
use its reasonable efforts to make available senior executives of the Company to participate in customary “road show”
presentations that may be reasonably requested by the Underwriter in any Underwritten Offering; and


3.1.16   
otherwise, in good faith, cooperate reasonably with, and take such customary actions as may reasonably be requested by the
Holders, in connection with such Registration, including, without limitation, making available senior executives of the Company
to participate in any due diligence sessions that may be reasonably requested by the Underwriter in any Underwritten Offering.


3.2.           
Registration Expenses. The Registration Expenses of all Registrations shall be borne by the Company. It is acknowledged
by the Holders that the Holders shall bear all incremental selling expenses relating to the sale of Registrable Securities, such
as Underwriters’ commissions and discounts, brokerage fees, Underwriter marketing costs and, other than as set forth in the
definition of “Registration Expenses,” all reasonable fees and expenses of any legal counsel representing the Holders.


3.3.           
Requirements for Participation in Underwritten Offerings. No person may participate in any Underwritten Offering
for equity securities of the Company pursuant to a Registration initiated by the Company hereunder unless such person (i) agrees
to sell such person’s securities on the basis provided in any underwriting arrangements approved by the Company and (ii)
completes and executes all customary questionnaires, powers of attorney, indemnities, lock-up agreements, underwriting agreements
and other customary documents as may be reasonably required under the terms of such underwriting arrangements.


3.4.            Suspension
of Sales; Adverse Disclosure. Upon receipt of written notice from the Company that a Registration Statement or Prospectus
contains a Misstatement, each of the Holders shall forthwith discontinue disposition of Registrable Securities until he, she
or it has received copies of a supplemented or amended Prospectus correcting the Misstatement (it being understood that the
Company hereby covenants to prepare and file such supplement or amendment as soon as practicable after the time of such
notice), or until he, she or it is advised in writing by the Company that the use of the Prospectus may be resumed. If the
filing, initial effectiveness or continued use of a Registration Statement in respect of any Registration at any time would
require the Company to make an Adverse Disclosure or would require the inclusion in such Registration Statement of financial
statements that are unavailable to the Company for reasons beyond the Company’s control, the Company may, upon giving
prompt written notice of such action to the Holders, delay the filing or initial effectiveness
of, or suspend use of, such Registration Statement for the shortest period of time, but in no event more than thirty (30) days,
determined in good faith by the Company to be necessary for such purpose. In the event the Company exercises its rights under the
preceding sentence, the Holders agree to suspend, immediately upon their receipt of the notice referred to above, their use of
the Prospectus relating to any Registration in connection with any sale or offer to sell Registrable Securities. The Company shall
immediately notify the Holders of the expiration of any period during which it exercised its rights under this Section 3.4.




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3.5.           
Reporting Obligations. As long as any Holder shall own Registrable Securities, the Company, at all times while it
shall be a reporting company under the Exchange Act, covenants to file timely (or obtain extensions in respect thereof and file
within the applicable grace period) all reports required to be filed by the Company after the date hereof pursuant to Sections
13(a) or 15(d) of the Exchange Act and to promptly furnish the Holders with true and complete copies of all such filings. The Company
further covenants that it shall take such further action as any Holder may reasonably request, all to the extent required from
time to time to enable such Holder to sell Ordinary Shares held by such Holder without registration under the Securities Act within
the limitation of the exemptions provided by Rule 144 promulgated under the Securities Act (or any successor rule promulgated thereafter
by the Commission), including providing any legal opinions. Upon the request of any Holder, the Company shall deliver to such Holder
a written certification of a duly authorized officer as to whether it has complied with such requirements.


ARTICLE IV

INDEMNIFICATION AND CONTRIBUTION


4.1.           
Indemnification.


4.1.1       
The Company agrees to indemnify, to the extent permitted by law, each Holder of Registrable Securities, its officers and
directors and each person who controls such Holder (within the meaning of the Securities Act) against all losses, claims, damages,
liabilities and expenses (including attorneys’ fees) caused by any untrue or alleged untrue statement of material fact contained
in any Registration Statement, Prospectus or preliminary Prospectus or any amendment thereof or supplement thereto or any omission
or alleged omission of a material fact required to be stated therein or necessary to make the statements therein not misleading,
except insofar as the same are caused by or contained in any information furnished in writing to the Company by such Holder expressly
for use therein. The Company shall indemnify the Underwriters, their officers and directors and each person who controls such Underwriters
(within the meaning of the Securities Act) to the same extent as provided in the foregoing with respect to the indemnification
of the Holder.


4.1.2       
In connection with any Registration Statement in which a Holder of Registrable Securities is participating, such Holder
shall furnish to the Company in writing such information and affidavits as the Company reasonably requests for use in connection
with any such Registration Statement or Prospectus and, to the extent permitted by law, shall indemnify the Company, its directors
and officers and agents and each person who controls the Company (within the meaning of the Securities Act) against any losses,
claims, damages, liabilities and expenses (including without limitation reasonable attorneys’ fees) resulting from any untrue
statement of material fact contained in the Registration Statement, Prospectus or preliminary Prospectus or any amendment thereof
or supplement thereto or any omission of a material fact required to be stated therein or necessary to make the statements therein
not misleading, but only to the extent that such untrue statement or omission is contained in any information or affidavit so furnished
in writing by such Holder expressly for use therein; provided, however, that the obligation to indemnify shall be
several, not joint and several, among such Holders of Registrable Securities, and the liability of each such Holder of Registrable
Securities shall be in proportion to and limited to the net proceeds received by such Holder from the sale of Registrable Securities
pursuant to such Registration Statement. The Holders of Registrable Securities shall indemnify the Underwriters, their officers,
directors and each person who controls such Underwriters (within the meaning of the Securities Act) to the same extent as provided
in the foregoing with respect to indemnification of the Company.




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4.1.3       
Any person entitled to indemnification herein shall (i) give prompt written notice to the indemnifying party of any claim
with respect to which it seeks indemnification (provided that the failure to give prompt notice shall not impair any person’s
right to indemnification hereunder to the extent such failure has not materially prejudiced the indemnifying party) and (ii) unless
in such indemnified party’s reasonable judgment a conflict of interest between such indemnified and indemnifying parties
may exist with respect to such claim, permit such indemnifying party to assume the defense of such claim with counsel reasonably
satisfactory to the indemnified party. If such defense is assumed, the indemnifying party shall not be subject to any liability
for any settlement made by the indemnified party without its consent (but such consent shall not be unreasonably withheld). An
indemnifying party who is not entitled to, or elects not to, assume the defense of a claim shall not be obligated to pay the fees
and expenses of more than one counsel for all parties indemnified by such indemnifying party with respect to such claim, unless
in the reasonable judgment of any indemnified party a conflict of interest may exist between such indemnified party and any other
of such indemnified parties with respect to such claim. No indemnifying party shall, without the consent of the indemnified party,
consent to the entry of any judgment or enter into any settlement which cannot be settled in all respects by the payment of money
(and such money is so paid by the indemnifying party pursuant to the terms of such settlement) or which settlement does not include
as an unconditional term thereof the giving by the claimant or plaintiff to such indemnified party of a release from all liability
in respect to such claim or litigation.


4.1.4       
The indemnification provided for under this Agreement shall remain in full force and effect regardless of any investigation
made by or on behalf of the indemnified party or any officer, director or controlling person of such indemnified party and shall
survive the transfer of securities. The Company and each Holder of Registrable Securities participating in an offering also agrees
to make such provisions as are reasonably requested by any indemnified party for contribution to such party in the event the Company’s
or such Holder’s indemnification is unavailable for any reason.




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4.1.5       
 If the indemnification provided under Section 4.1 hereof from the indemnifying party is unavailable or insufficient
to hold harmless an indemnified party in respect of any losses, claims, damages, liabilities and expenses referred to herein, then
the indemnifying party, in lieu of indemnifying the indemnified party, shall contribute to the amount paid or payable by the indemnified
party as a result of such losses, claims, damages, liabilities and expenses in such proportion as is appropriate to reflect the
relative fault of the indemnifying party and the indemnified party, as well as any other relevant equitable considerations. The
relative fault of the indemnifying party and indemnified party shall be determined by reference to, among other things, whether
any action in question, including any untrue or alleged untrue statement of a material fact or omission or alleged omission to
state a material fact, was made by, or relates to information supplied by, such indemnifying party or indemnified party, and the
indemnifying party’s and indemnified party’s relative intent, knowledge, access to information and opportunity to correct
or prevent such action; provided, however, that the liability of any Holder under this subsection 4.1.5 shall
be limited to the amount of the net proceeds received by such Holder in such offering giving rise to such liability. The amount
paid or payable by a party as a result of the losses or other liabilities referred to above shall be deemed to include, subject
to the limitations set forth in subsections 4.1.1, 4.1.2 and 4.1.3 above, any legal or other fees, charges
or expenses reasonably incurred by such party in connection with any investigation or proceeding. The parties hereto agree that
it would not be just and equitable if contribution pursuant to this subsection 4.1.5 were determined by pro rata allocation
or by any other method of allocation, which does not take account of the equitable considerations referred to in this subsection
4.1.5. No person guilty of fraudulent misrepresentation (within the meaning of Section 11(f) of the Securities Act) shall be
entitled to contribution pursuant to this subsection 4.1.5 from any person who was not guilty of such fraudulent misrepresentation.


ARTICLE V

MISCELLANEOUS


5.1.           
Notices. Any notice or communication under this Agreement must be in writing and given by (i) deposit in the United
States mail, addressed to the party to be notified, postage prepaid and registered or certified with return receipt requested,
(ii) delivery in person or by courier service providing evidence of delivery, or (iii) transmission by hand delivery, electronic
mail or facsimile. Each notice or communication that is mailed, delivered or transmitted in the manner described above shall be
deemed sufficiently given, served, sent, and received, in the case of mailed notices, on the third business day following the date
on which it is mailed and, in the case of notices delivered by courier service, hand delivery, electronic mail or facsimile, at
such time as it is delivered to the addressee (with the delivery receipt or the affidavit of messenger) or at such time as delivery
is refused by the addressee upon presentation. Any notice or communication under this Agreement must be addressed, if to the Company,
to: 9 West 57th Street, 43rd Floor New York, NY 10019, or by email at: jcrossen@apollo.com. Any party may
change its address for notice at any time and from time to time by written notice to the other parties hereto, and such change
of address shall become effective thirty (30) days after delivery of such notice as provided in this Section 5.1.




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5.2.           
 Assignment; No Third Party Beneficiaries.


5.2.1       
This Agreement and the rights, duties and obligations of the Company hereunder may not be assigned or delegated by the Company
in whole or in part.


5.2.2       
A Holder may assign or delegate such Holder’s rights, duties or obligations under this Agreement, in whole or in part,
to a Permitted Transferee who agrees to become bound by the transfer restrictions set forth in this Agreement.


5.2.3       
This Agreement and the provisions hereof shall be binding upon and shall inure to the benefit of each of the parties and
its successors and the permitted assigns of the Holders, which shall include Permitted Transferees.


5.2.4       
This Agreement shall not confer any rights or benefits on any persons that are not parties hereto, other than as expressly
set forth in this Agreement and Section 5.2 hereof.


5.2.5       
No assignment by any party hereto of such party’s rights, duties and obligations hereunder shall be binding upon or
obligate the Company unless and until the Company shall have received (i) written notice of such assignment as provided in Section
5.1 hereof and (ii) the written agreement of the assignee, in a form reasonably satisfactory to the Company, to be bound by
the terms and provisions of this Agreement (which may be accomplished by an addendum or certificate of joinder to this Agreement).
Any transfer or assignment made other than as provided in this Section 5.2 shall be null and void.


5.3.           
Counterparts. This Agreement may be executed in multiple counterparts (including facsimile or PDF counterparts),
each of which shall be deemed an original, and all of which together shall constitute the same instrument, but only one of which
need be produced.


5.4.           
Governing Law; Venue. NOTWITHSTANDING THE PLACE WHERE THIS AGREEMENT MAY BE EXECUTED BY ANY OF THE PARTIES HERETO,
THE PARTIES EXPRESSLY AGREE THAT (I) THIS AGREEMENT SHALL BE GOVERNED BY AND CONSTRUED UNDER THE LAWS OF THE STATE OF NEW YORK
AS APPLIED TO AGREEMENTS AMONG NEW YORK RESIDENTS ENTERED INTO AND TO BE PERFORMED ENTIRELY WITHIN NEW YORK, WITHOUT REGARD TO
THE CONFLICT OF LAW PROVISIONS OF SUCH JURISDICTION AND (II) THE VENUE FOR ANY ACTION TAKEN WITH RESPECT TO THIS AGREEMENT SHALL
BE ANY STATE OR FEDERAL COURT IN NEW YORK COUNTY IN THE STATE OF NEW YORK.


5.5.           
Amendments and Modifications. Upon the written consent of the Company and the Holders of at least fifty percent (50%)
of the Registrable Securities at the time in question, compliance with any of the provisions, covenants and conditions set forth
in this Agreement may be waived, or any of such provisions, covenants or conditions may be amended or modified; provided,
however, that notwithstanding the foregoing, any amendment hereto or waiver hereof that adversely
affects one Holder, solely in his, her or its capacity as a holder of Ordinary Shares of the Company, in a manner that is materially
different from the other Holders (in such capacity) shall require the consent of the Holder so affected. No course of dealing between
any Holder or the Company and any other party hereto or any failure or delay on the part of a Holder or the Company in exercising
any rights or remedies under this Agreement shall operate as a waiver of any rights or remedies of any Holder or the Company. No
single or partial exercise of any rights or remedies under this Agreement by a party shall operate as a waiver or preclude the
exercise of any other rights or remedies hereunder or thereunder by such party.




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5.6.           
Other Registration Rights. The Company represents and warrants that no person, other than a Holder of Registrable
Securities, has any right to require the Company to register any securities of the Company for sale or to include such securities
of the Company in any Registration filed by the Company for the sale of securities for its own account or for the account of any
other person. Further, the Company represents and warrants that this Agreement supersedes any other registration rights agreement
or agreement with similar terms and conditions and in the event of a conflict between any such agreement or agreements and this
Agreement, the terms of this Agreement shall prevail.


5.7.           
Term. This Agreement shall terminate upon the earlier of (i) the tenth anniversary of the date of this Agreement
or (ii) the date as of which (A) all of the Registrable Securities have been sold pursuant to a Registration Statement (but in
no event prior to the applicable period referred to in Section 4(a)(3) of the Securities Act and Rule 174 thereunder (or any successor
rule promulgated thereafter by the Commission)) or (B) the Holders of all Registrable Securities are permitted to sell the Registrable
Securities under Rule 144 (or any similar provision) under the Securities Act without limitation on the amount of securities sold
or the manner of sale. The provisions of Section 3.5 and Article IV shall survive any termination.


[SIGNATURE PAGES FOLLOW]




    19


     


    

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


	 	COMPANY:
	 	 	 	 
	 	APOLLO STRATEGIC GROWTH CAPITAL III
	 	a Cayman Islands exempted company, incorporated with limited liability
	 	 	 	 
	 	By:	
	 	 	Name: 	James Crossen
	 	 	Title:	Chief Financial Officer, Chief Accounting Officer and Secretary
	 	 	 	 



 


	 	HOLDER:
	 	 	 	 
	 	APSG SPONSOR III, L.P.
	 	 	 	 
	 	By: AP Caps II Holdings GP, LLC, its general partner
	 	 
	 	By: Apollo Principal Holdings
III, L.P., its managing member
	 	 
	 	By: Apollo Principal Holdings
III GP, Ltd., its general partner
	 	 
	 	By:	 
	 	 	Name:

                                                                      Title:









 


[Signature Page to Registration Rights Agreement]



    


     


    

 





 


 


	 	HOLDER:
	 	 
	 	By:
	 	 
	 	 
	 	 
	 	[__________]
	 	 
	 	 
	 	 
	 	[__________]
	 	 
	 	
         

         

	 	[__________]


 


[Signature Page to Registration Rights Agreement]