Exhibit
4.13



Execution Version – February 27, 2024



LETTER
AGREEMENT

RELATING
TO

SHARE
SUBSCRIPTION FACILITY



This
Letter Agreement (the “Letter Agreement”), is made as of February 27, 2024, by and between CRITICAL METALS CORP.,
a BVI business company incorporated in the British Virgin Islands (the “Company”); GEM GLOBAL YIELD LLC SCS, a “société
en commandite simple” formed under the laws of Luxembourg (the “Purchaser”); and GEM YIELD BAHAMAS LIMITED,
a limited company formed under the laws of the Commonwealth of the Bahamas (“GYBL,” and together with the Company
and Purchaser, the “Parties”). Defined terms used but not otherwise defined herein shall have the meanings given to
such terms in the Share Purchase Agreement (as defined below).



WHEREAS,the Parties are parties to that certain Share Purchase Agreement, dated as of July 4, 2023 (the “Share Purchase Agreement”),
which includes a form of Warrant, which shall be issued on the Public Listing Date pursuant to Section 4.12(b) of the Share Purchase
Agreement; and



WHEREAS,the Company has requested that the Purchaser agree to restrict sales of shares issuable pursuant to exercise of the Warrant (as defined
below) for a period of 12 months after the Public Listing Date (the “Lock-Up”);



NOW
THEREFORE, for good and valuable consideration, the receipt of which is hereby acknowledged, the Parties hereto hereby agree as follows:



1. The
Purchaser agrees to the Lock-Up, subject to the Company’s agreement to the terms of this Letter Agreement.



2. On
the Public Listing Date, the Company shall provide Common Shares to the Purchaser in respect of the Commitment Fee (the “Commitment
Shares”) pursuant to Section 4.12(d) of the Share Purchase Agreement. On the 61st day after the Public Listing Date,
the Purchaser shall have at its sole discretion, the option to sell such shares to the Company for $1.875 million in immediately available
funds payable in USD by wire payment to an account designated by the Purchaser in writing. The Company’s failure to deliver such
$1.875 million payment within twenty-four hours of notification by the Purchaser shall incur a daily penalty of 10% of such amount, compounded
daily, payable in USD. If the Purchaser does not exercise such option, then the original terms of the Share Purchase Agreement shall
govern the payment of the Commitment Fee.



3. The
Purchaser may exercise the Warrant for Common Shares pursuant to the terms thereof but shall not sell such Common Shares during the Lock-Up
period.













4. On
the first anniversary of the Public Listing Date, the Purchaser shall have the right to require the Company to purchase, and the Company
agrees to purchase, the Warrant from the Purchaser in exchange for a number of Common Shares having a value equal to $27,200,000. For
this purpose, the value of the Common Shares shall be the closing bid price of the Common Shares, as reported by Bloomberg, as of the
close of market on the day that the Purchaser exercises its right pursuant to this paragraph 4. Such Common Shares issued pursuant to
this paragraph 4 shall be unrestricted and freely tradable. The Company’s failure to either (i) instruct its transfer agent to
issue such Common Shares within 1 business day of notification by the Purchaser or (ii) deliver such Common Shares within 3 business
days of notification by the Purchaser, in each case, shall incur a daily penalty of 15% of such amount, compounded daily, payable in
USD.



5. This
Agreement shall be governed by and construed in accordance with the internal laws of the State of New York, without giving effect to
the choice of law provisions except Section 5-1401 of the New York General Obligations Law.



6. The
Letter Agreement may not be amended nor may any provision hereof be waived without the express written consent of the Parties.



7. This
Letter Agreement may be executed in any number of counterparts (including by facsimile or other electronic transmission), each of which
shall be deemed an original, but all of which taken together shall constitute one and the same instrument, and the Parties hereto may
execute this Letter Agreement by signing any such counterpart.



[signature
page follows]







2







IN
WITNESS WHEREOF, the Parties hereto have caused this Letter Agreement to be duly executed by their respective authorized officer
as of the date first above written.



| | CRITICAL
    METALS CORP.   
| | ----------------------------
| |                             
| | By:                         
| | Name:                       
| | Title:                      
| |                             
| | GEM
    GLOBAL YIELD LLC SCS
| |                             
| | By:                         
| | Name:                       
| | Title:                      
| |                             
| | GEM
    YIELD BAHAMAS LTD.  
| |                             
| | By:                         
| | Name:                       
| | Title:                      





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