Document:

Exhibit 4.1

  

Annex B

 

Face of Certificate - ZION OIL & GAS,
INC.]

 

(SEE REVERSE SIDE FOR LEGEND)

 

W

 

WARRANTS

 

(THIS WARRANT WILL BE VOID IF NOT EXERCISED
PRIOR TO 5:00 P.M., EASTERN

STANDARD TIME, January 31, 2020)

 

ZION OIL & GAS, INC.

 

CUSIP 989696 141

 

WARRANT

 

THIS CERTIFIES THAT, for value received _____________ is the registered
holder of a Warrant or Warrants expiring January 31, 2020 (the "Warrant") to purchase one fully paid and non-assessable
share of Common Stock, par value $.01 per share (the "Shares"), of ZION OIL & GAS, INC., a Delaware corporation (the
"Company"). The Warrant entitles the holder thereof to purchase from the Company, commencing on January 31, 2015, one
Share of the Company at the price of $2.00 per share, upon surrender of this Warrant Certificate and payment of the Warrant Price
at the office or agency of the Warrant Agent, American Stock Transfer & Trust Company, LLC (such payment to be made by check
made payable to the order of the Company), but only subject to the conditions set forth herein and in the Warrant Agreement between
the Company and the Warrant Agent. In no event shall the registered holder of this Warrant be entitled to receive a net-cash settlement
or other consideration in lieu of physical settlement in Shares of the Company. The Warrant Agreement provides that, upon the occurrence
of certain events, the Warrant Price and the number of Warrant Shares purchasable hereunder, set forth on the face hereof, may,
subject to certain conditions, be adjusted. The term Warrant Price as used in this Warrant Certificate refers to the price per
Share at which Shares may be purchased at the time the Warrant is exercised.

 

This Warrant may expire on the date first above written if it is
not exercised prior to such date by the registered holder pursuant to the terms of the Warrant Agreement.

 

No fraction of a Share will be issued upon any exercise of a Warrant.
If, upon exercise of a Warrant, a holder would be entitled to receive a fractional interest in a Share, the Company will, upon
exercise, round up to the nearest whole number the number of shares of common stock to be issued to the warrant holder.

 

Upon any exercise of the Warrant for less than the total number
of full Shares provided for herein, there shall be issued to the registered holder hereof or his/her/its assignee a new Warrant
Certificate covering the number of Shares for which the Warrant has not been exercised.

 

Warrant Certificates, when surrendered at the office or agency of
the Warrant Agent by the registered holder hereof in person or by 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 and evidencing in the aggregate a like number of Warrants.

 

    	 

    	 

    

 

Upon due presentment for registration of transfer
of the Warrant Certificate at the office or agency 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 in exchange for this Warrant
Certificate, subject to the limitations provided in the Warrant Agreement, without charge except for any applicable tax or other
governmental charge.

 

The Company and the Warrant Agent may deem
and treat the registered holder as the absolute owner of the Warrants represented by 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 registered holder, and for all other purposes, and neither the Company nor the Warrant Agent shall be affected by any notice
to the contrary.

 

 

This Warrant does not entitle the registered holder to any of the
rights of a stockholder of the Company.

  

COUNTERSIGNED:

American Stock Transfer & Trust Company,
LLC

 

WARRANT AGENT

BY:

AUTHORIZED OFFICER

 

DATED:

 

(Signature)

CHIEF EXECUTIVE OFFICER

 

(Seal)

 

(Signature)

SECRETARY

 

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SUBSCRIPTION FORM

 

To Be Executed by the Registered Holder in Order
to Exercise Warrants

 

The undersigned Registered Holder irrevocably elects to exercise
_________ Warrants represented by this Warrant Certificate, and to purchase the shares of Common Stock issuable upon the exercise
of such Warrants, and requests that Certificates for such shares shall be issued in the name of

 

(PLEASE TYPE OR PRINT NAME AND ADDRESS)

 

(SOCIAL SECURITY OR TAX IDENTIFICATION NUMBER)

 

and be delivered to

(PLEASE PRINT OR TYPE NAME AND ADDRESS)

 

and, if such number of Warrants shall not be all the Warrants evidenced
by this Warrant Certificate, that a new Warrant Certificate for the balance of such Warrants be registered in the name of, and
delivered to, the Registered Holder at the address stated below:

 

Dated:

  

 

(SIGNATURE)

 

 

(ADDRESS)

  

 

 

 

 

 (TAX IDENTIFICATION
NUMBER)

 

THE SIGNATURE TO THE ASSIGNMENT OF THE SUBSCRIPTION FORM MUST CORRESPOND
TO THE NAME WRITTEN UPON THE FACE OF THIS WARRANT CERTIFICATE IN EVERY PARTICULAR, WITHOUT ALTERATION OR ENLARGEMENT OR ANY CHANGE
WHATSOEVER, AND MUST BE GUARANTEED BY A COMMERCIAL BANK OR TRUST COMPANY OR A MEMBER FIRM OF THE AMERICAN STOCK EXCHANGE, NEW YORK
STOCK EXCHANGE, PACIFIC STOCK EXCHANGE OR CHICAGO STOCK EXCHANGE.

 

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ASSIGNMENT

 

To Be Executed by the Registered Holder in Order to Assign Warrants

 

For Value Received,_____________________hereby sell, assign, and
transfer unto

 

 

 

(PLEASE TYPE OR PRINT NAME AND ADDRESS)

 

 

 

 

(SOCIAL SECURITY OR TAX IDENTIFICATION NUMBER)

 

and be delivered to

 

 

(PLEASE PRINT OR TYPE NAME AND ADDRESS)

 

 

 

Of the Warrants represented by this Warrant Certificate, and hereby
irrevocably constitute and

 

appoint________________________________Attorney to transfer this
Warrant Certificate on the books of the Company, with full power of substitution in the premises.

 

Dated:

 

 

(SIGNATURE)

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.

 

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).

 

 

 

4Exhibit 4.2

 

WARRANT AGREEMENT

 

This Warrant Agreement (this "Agreement")
is made as of August 1, 2014, by and between Zion Oil & Gas, Inc., a Delaware corporation having its principal place of business
at 6510 Abrams Road, Suite 300, Dallas, Texas 75231 (the "Company"), and American Stock Transfer &
Trust Company, LLC, a New York limited liability trust company with offices at 6201 15th Avenue, Brooklyn, NY 11219
(”AST").

 

WHEREAS, the Company has implemented a Dividend
Reinvestment and Common Stock Purchase Plan (hereinafter “DSPP”) and AST is administering the DSPP, effective
August 1, 2014;

 

WHEREAS, pursuant to the DSPP, the Company is
offering units (each a “Unit” and collectively the “Units”) of its securities
to existing stockholders and investors, with each Unit consisting of (i) one (1) share of the Company’s common stock, par
value $0.01 per share (the “Common Stock”), and (ii) one (1) warrant to purchase one additional share
of the Company’s Common Stock at an exercise price of $2.00 per share (each “Warrant” and collectively
the “Warrants”); Each Unit may be purchased currently at a per Unit price of $2.50; and

 

WHEREAS, the Warrant will be exercisable for
a five (5) year period beginning on January 31, 2015; and

 

WHEREAS, the Company is utilizing the Registration
Statement on Form S-3 (Registration No. 333-193336), as amended, which was declared effective by the SEC on March 27, 2014 (the
“Registration Statement”) to facilitate the trading of the shares of Common Stock included in the Units
and the shares of Common Stock underlying the Warrants that are included in the Units as well as the Warrants; and

 

WHEREAS, the shares of Common Stock included
in the Units are tradable on the NASDAQ under the symbol ZN and, following the closing of the Unit program, the shares of Common
Stock underlying the Warrants, will be tradable after Warrant exercise on the NASDAQ under the symbol ZN; the Company has filed
an application to list the Warrants on the NASDAQ; the Units will not be listed for trading nor will they otherwise be tradable;
and

 

WHEREAS, the Company desires AST to act on behalf
of the Company, and AST is willing to so act, in connection with the issuance, registration, transfer, exchange, redemption and
exercise of the Warrants (in such capacity, the “Warrant Agent”); and

 

WHEREAS, the Company desires to provide for
the form and provisions of the Warrants, the terms upon which they shall be issued and exercised, and the respective rights, limitation
of rights, and immunities of the Company, the Warrant Agent, and the holders of the Warrants; and

 

WHEREAS, all acts and things have been done
and performed which are necessary to make the Warrants, when executed on behalf of the Company and countersigned by or on behalf
of the Warrant Agent, as provided herein, the valid, binding and legal obligations of the Company, and to authorize the execution
and delivery of this Agreement.

 

    	 

    	 

    

 

NOW, THEREFORE, in consideration of the mutual
agreements herein contained, the parties hereto agree as follows:

 

1.      Appointment of Warrant Agent. The Company hereby
appoints the Warrant Agent to act as agent for the Company for the Warrants, and the Warrant Agent hereby accepts such
appointment and agrees to perform the same in accordance with the terms and conditions set forth in this Agreement.

 

2.      Warrants.

 

2.1    Form of Warrant. Each Warrant shall be issued in registered
form only. The Warrants shall be in substantially the form of Exhibit A hereto, the provisions of which are incorporated
herein, and shall be signed by, or bear the facsimile signature of, the Executive Chairman and Secretary/Treasurer of the Company
and shall bear a facsimile of the Company's seal. In the event the person whose facsimile signature has been placed upon any Warrant
shall have ceased to serve in the capacity in which such person signed the Warrant before such Warrant is issued, it may be issued
with the same effect as if he or she had not ceased to be such at the date of issuance.

 

2.2    Effect of Countersignature. Unless and until countersigned
by the Warrant Agent pursuant to this Agreement, a Warrant shall be invalid and of no effect and may not be exercised by the holder
thereof.

 

2.3    Registration.

 

2.3.1 Warrant Register. The Warrant Agent shall maintain
books ("Warrant Register") for the registration of original issuance and the registration of transfer of
the Warrants. Upon the initial issuance of the Warrants, the Warrant Agent shall issue and register the Warrants in the names of
the respective holders thereof in such denominations and otherwise in accordance with instructions delivered to the Warrant Agent
by the Company.

 

2.3.2 Registered Holder. Prior to due presentment for registration
of transfer of any Warrant, the Company and the Warrant Agent may deem and treat the person in whose name such Warrant shall be
registered upon the Warrant Register ("registered holder"), as the absolute owner of such Warrant and of
each Warrant represented thereby (notwithstanding any notation of ownership or other writing on the Warrant Certificate made by
anyone other than the Company or the Warrant Agent), for the purpose of any exercise thereof, and for all other purposes, and neither
the Company nor the Warrant Agent shall be affected by any notice to the contrary.

 

3.      Terms and Exercise of Warrants.

 

3.1    Warrant Price. Each Warrant shall, when countersigned
by the Warrant Agent, entitle the registered holder thereof, subject to the provisions of such Warrant and this Warrant Agreement,
to purchase from the Company the number of shares of Common Stock stated therein, at the price of $2.00 per share, subject to the
adjustments provided in this Section 3.1 and Section 4 hereof. The term "Warrant Price" as used in this Warrant Agreement
refers to the price per share at which Common Stock may be purchased at the time a Warrant is exercised. The Company in its sole
discretion may lower the Warrant Price at any time prior to the Expiration Date for a period of not less than ten business days,
provided that any such reduction shall be identical among all of the Warrants.

 

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3.2    Duration of Warrants. A Warrant may be exercised only
during the period commencing on January 31, 2015 and terminating at 5:00 p.m., Eastern Standard Time on the fifth anniversary thereof.
Notwithstanding the foregoing, no Warrant shall be exercisable unless, at the time of exercise, a registration statement relating
to the Common Stock issuable upon the exercise of such Warrant is effective and current and a prospectus is available for use by
the holders thereof and the Common Stock has been qualified or deemed to be exempt under the securities laws of the state of residence
of the holder of such Warrants. The period during which a Warrant may be exercised shall be deemed the "Exercise Period"
and the termination of such Exercise Period shall be deemed the "Expiration Date." Each Warrant not exercised
on or before the Expiration Date shall become void, and all rights thereunder and all rights in respect thereof under this Agreement
shall cease at the close of business on the Expiration Date. The Company in its sole discretion may extend the duration of the
Warrants by delaying the Expiration Date; provided, however, the Company will provide notice to registered holders of the Warrants
of such extension of not less than 20 days and, further provided that any such extension shall be identical in duration among all
of the Warrants.

 

3.3    Exercise of Warrants.

 

3.3.1 Payment. Subject to the provisions of the Warrants
and this Warrant Agreement, a Warrant, when countersigned by the Warrant Agent, may be exercised by the registered holder thereof
by surrendering it at the office of the Warrant Agent, or at the office of its successor as Warrant Agent, in Brooklyn, New York,
with the subscription form, as set forth in the Warrant, duly executed by paying in full, by bank check, bank wire, other electronic
bank payment method, or other legal currency means of payment acceptable by the Company and payable to the order of the Company,
the Warrant Price for each full share of Common Stock as to which the Warrant is exercised and any and all applicable taxes due
in connection with the exercise of the Warrant, the exchange of the Warrant for the Common Stock and the issuance of the Common
Stock.

 

3.3.2 Issuance of Certificates. As soon as practicable after
the exercise of any Warrant and the clearance of the funds in payment of the Warrant Price, the Company shall issue to the registered
holder of such Warrant a certificate or certificates for the number of full shares of Common Stock to which he, she or it is entitled,
registered in such name or names as may be directed by him, her or it, and if such Warrant shall not have been exercised in full,
a new countersigned Warrant for the number of shares as to which such Warrant shall not have been exercised. Notwithstanding the
foregoing, the Company shall not be obligated to deliver any securities pursuant to the exercise of a Warrant unless (i) a registration
statement under the Act with respect to the Common Stock issuable upon such exercise is effective, or (ii) in the opinion of counsel
to the Company, the exercise of the Warrants is exempt from the registration requirements of the Act and such securities are qualified
for sale or exempt from qualification under applicable securities laws of the states or other jurisdictions in which the registered
holders reside. Warrants may not be exercised by, or securities issued to, any registered holder in any state in which such exercise
or issuance would be unlawful. In no event will the Company be required to provide the registered holder of a warrant with a net-cash
settlement or other consideration in lieu of physical settlement in shares of Common Stock, regardless of whether the Common Stock
underlying the Warrants is registered pursuant to an effective registration statement.

 

3.3.3 Valid Issuance. All shares of Common Stock issued upon
the proper exercise of a Warrant in conformity with this Agreement shall be validly issued, fully paid and nonassessable.

 

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3.3.4 Date of Issuance. Each person in whose name any such
certificate for shares of Common Stock is issued shall for all purposes be deemed to have become the holder of record of such shares
on the date on which the Warrant was surrendered and payment of the Warrant Price was made, irrespective of the date of delivery
of such certificate, except that, if the date of such surrender and payment is a date when the stock transfer books of the Company
are closed, such person shall be deemed to have become the holder of such shares at the close of business on the next succeeding
date on which the stock transfer books are open.

 

4.      Adjustments.

 

4.1    Stock Dividends Split Ups. If after the date hereof,
and subject to the provisions of Section 4.6 below, the number of outstanding shares of Common Stock is increased by a stock dividend
payable in shares of Common Stock, or by a split up of shares of Common Stock, or other similar event, then, on the effective date
of such stock dividend, split up or similar event, the number of shares of Common Stock issuable on exercise of each Warrant shall
be increased in proportion to such increase in outstanding shares of Common Stock. For purposes of clarification, no adjustment
shall be made in the event of a rights offering or similar transaction.

 

4.2    Aggregation of Shares. If after the date hereof, and
subject to the provisions of Section 4.6, the number of outstanding shares of Common Stock is decreased by a consolidation, combination,
reverse stock split or reclassification of shares of Common Stock or other similar event, then, on the effective date of such consolidation,
combination, reverse stock split, reclassification or similar event, the number of shares of Common Stock issuable on exercise
of each Warrant shall be decreased in proportion to such decrease in outstanding shares of Common Stock.

 

4.3    Adjustments in Exercise Price. Whenever the number of
shares of Common Stock purchasable upon the exercise of the Warrants is adjusted, as provided in Section 4.1 and 4.2 above, the
Warrant Price shall be adjusted (to the nearest cent) by multiplying such Warrant Price immediately prior to such adjustment by
a fraction (x) the numerator of which shall be the number of shares of Common Stock purchasable upon the exercise of the Warrants
immediately prior to such adjustment, and (y) the denominator of which shall be the number of shares of Common Stock so purchasable
immediately thereafter.

 

4.4    Replacement of Securities upon Reorganization,
etc. In case of any reclassification or reorganization of the outstanding shares of Common Stock (other than a change covered
by Section 4.1 or 4.2 hereof or that solely affects the par value of such shares of Common Stock), or in the case of any merger
or consolidation of the Company with or into another corporation (other than a consolidation or merger in which the Company is
the continuing corporation and that does not result in any reclassification or reorganization of the outstanding shares of Common
Stock), or in the case of any sale or conveyance to another corporation or entity of the assets or other property of the Company
as an entirety or substantially as an entirety in connection with which the Company is dissolved, the Warrant holders shall thereafter
have the right to purchase and receive, upon the basis and upon the terms and conditions specified in the Warrants and in lieu
of the shares of Common Stock of the Company immediately theretofore purchasable and receivable upon the exercise of the rights
represented thereby, the kind and amount of shares of stock or other securities or property (including cash) receivable upon such
reclassification, reorganization, merger or consolidation, or upon a dissolution following any such sale or transfer, that the
Warrant holder would have received if such Warrant holder had exercised his, her or its Warrant(s) immediately prior to such event;
and if any reclassification also results in a change in shares of Common Stock covered by Section 4.1 or 4.2, then such adjustment
shall be made pursuant to Sections 4.1, 4.2, 4.3 and this Section 4.4. The provisions of this Section 4.4 shall similarly apply
to successive reclassifications, reorganizations, mergers or consolidations, sales or other transfers.

 

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4.5    Notices of Changes in Warrant. Upon every adjustment
of the Warrant Price or the number of shares issuable on exercise of a Warrant, the Company shall give written notice thereof to
the Warrant Agent, which notice shall state the Warrant Price resulting from such adjustment and the increase or decrease, if any,
in the number of shares purchasable at such price upon the exercise of a Warrant, setting forth in reasonable detail the method
of calculation and the facts upon which such calculation is based. Upon the occurrence of any event specified in Sections 4.1,
4.2, 4.3 or 4.4, then, in any such event, the Company shall give written notice to the Warrant holder, at the last address set
forth for such holder in the Warrant Register, of the record date or the effective date of the event. Failure to give such notice,
or any defect therein, shall not affect the legality or validity of such event.

 

4.6    No Fractional Shares. Notwithstanding any provision contained
in this Warrant Agreement to the contrary, the Company shall not issue fractional shares upon exercise of Warrants. If, by reason
of any adjustment made pursuant to this Section 4, the holder of any Warrant would be entitled, upon the exercise of such Warrant,
to receive a fractional interest in a share, the Company shall, upon such exercise, round up to the nearest whole number the number
of the shares of Common Stock to be issued to the Warrant holder.

 

4.7    Form of Warrant. The form of Warrant need not be changed
because of any adjustment pursuant to this Section 4, and Warrants issued after such adjustment may state the same Warrant Price
and the same number of shares as is stated in the Warrants initially issued pursuant to this Agreement. However, the Company may
at any time in its sole discretion make any change in the form of Warrant that the Company may deem appropriate and that does not
affect the substance thereof, and any Warrant thereafter issued or countersigned, whether in exchange or substitution for an outstanding
Warrant or otherwise, may be in the form as so changed.

 

5.     Transfer and Exchange of Warrants.

 

5.1   Registration of Transfer. The Warrant Agent shall register
the transfer, from time to time, of any outstanding Warrant upon the Warrant Register, upon surrender of such Warrant for transfer,
properly endorsed with signatures properly guaranteed and accompanied by appropriate instructions for transfer. Upon any such transfer,
a new Warrant representing an equal aggregate number of Warrants shall be issued and the old Warrant shall be cancelled by the
Warrant Agent. The Warrants so cancelled shall be delivered by the Warrant Agent to the Company from time to time upon request.

 

5.2    Procedure for Surrender of Warrants. Warrants may be
surrendered to the Warrant Agent, together with a written request for exchange, and thereupon the Warrant Agent shall issue in
exchange therefor one or more new Warrants as requested by the registered holder of the Warrants so surrendered, representing an
equal aggregate number of Warrants; provided, however, in the event a Warrant surrendered for transfer bears a restrictive legend,
the Warrant Agent shall not cancel such Warrant and issue new Warrants in exchange therefor until the Warrant Agent has received
an opinion of counsel for the Company stating such transfer may be made and indicating whether the new Warrants must also bear
a restrictive legend.

 

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5.3    Fractional Warrants. The Warrant Agent shall not be required
to effect any registration of transfer or exchange which will result in the issuance of a warrant certificate for a fraction of
a warrant.

 

5.4    Service Charges. No service charge shall be made for
any exchange or registration of transfer of Warrants.

 

5.5    Warrant Execution and Countersignature. The Warrant Agent
is hereby authorized to countersign and deliver, in accordance with the terms of this Agreement, the Warrants required to be issued
pursuant to the provisions of this Section 5, and the Company, whenever required by the Warrant Agent, will supply the Warrant
Agent with Warrants duly executed on behalf of the Company for such purpose.

 

6.      Other Provisions Relating to Rights of Holders of Warrants.

 

6.1    No Rights as Stockholder. A Warrant does not entitle
the registered holder thereof to any of the rights of a stockholder of the Company, including, without limitation, the right to
receive dividends, or other distributions, exercise any preemptive rights to vote or to consent or to receive notice as stockholders
in respect of the meetings of stockholders or the election of directors of the Company or any other matter.

 

6.2    Lost, Stolen, Mutilated, or Destroyed Warrants. If any
Warrant is lost, stolen, mutilated, or destroyed, the Company and the Warrant Agent may on such terms as to indemnity or otherwise
as they may in their discretion impose (which shall, in the case of a mutilated Warrant, include the surrender thereof), issue
a new Warrant of like denomination, tenor, and date as the Warrant so lost, stolen, mutilated, or destroyed. Any such new Warrant
shall constitute a substitute contractual obligation of the Company, whether or not the allegedly lost, stolen, mutilated, or destroyed
Warrant shall be at any time enforceable by anyone.

 

6.3    Reservation of Common Stock. The Company shall at all
times reserve and keep available a number of its authorized but unissued shares of Common Stock that will be sufficient to permit
the exercise in full of all outstanding Warrants issued pursuant to this Warrant Agreement.

 

7.      Concerning the Warrant Agent and Other Matters.

 

7.1    Payment of Taxes. The Company will from time to time
promptly pay all taxes and charges that may be imposed upon the Company or the Warrant Agent in respect of the issuance or delivery
of shares of Common Stock upon the exercise of Warrants, but the Company shall not be obligated to pay any transfer taxes in respect
of the Warrants or such shares.

 
 

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7.2    Resignation, Consolidation, or Merger of Warrant Agent.

 

7.2.1 Appointment of Successor Warrant Agent. The Warrant
Agent, or any successor to it hereafter appointed, may resign its duties and be discharged from all further duties and liabilities
hereunder after giving sixty (60) days' notice in writing to the Company. If the office of the Warrant Agent becomes vacant by
resignation or incapacity to act or otherwise, the Company shall appoint in writing a successor Warrant Agent in place of the Warrant
Agent. If the Company shall fail to make such appointment within a period of 30 days after it has been notified in writing of such
resignation or incapacity by the Warrant Agent or by the holder of the Warrant (who shall, with such notice, submit his Warrant
for inspection by the Company), then the holder of any Warrant may apply to a court of competent jurisdiction for the appointment
of a successor Warrant Agent. Any successor Warrant Agent, whether appointed by the Company or by such court, shall be authorized
to exercise corporate trust powers and subject to supervision or examination by federal or state authority. After appointment,
any successor Warrant Agent shall be vested with all the authority, powers, rights, immunities, duties, and obligations of its
predecessor Warrant Agent with like effect as if originally named as Warrant Agent hereunder, without any further act or deed;
but if for any reason it becomes necessary or appropriate, the predecessor Warrant Agent shall execute and deliver, at the expense
of the Company, an instrument transferring to such successor Warrant Agent all the authority, powers, and rights of such predecessor
Warrant Agent hereunder; and upon request of any successor Warrant Agent the Company shall make, execute, acknowledge, and deliver
any and all instruments in writing for more fully and effectually vesting in and confirming to such successor Warrant Agent all
such authority, powers, rights, immunities, duties, and obligations.

 

7.2.2 Notice of Successor Warrant Agent.
In the event a successor Warrant Agent shall be appointed, the Company shall give notice thereof to the predecessor Warrant Agent
and the transfer agent for the Common Stock not later than the effective date of any such appointment.

 

7.2.3 Merger or Consolidation of Warrant Agent. Any corporation
into which the Warrant Agent may be merged or with which it may be consolidated or any corporation resulting from any merger or
consolidation to which the Warrant Agent shall be a party shall be the successor Warrant Agent under this Warrant Agreement without
any further act.

 

7.3    Fees and Expenses of Warrant Agent.

 

7.3.1 Remuneration. The Company agrees to pay the Warrant
Agent reasonable remuneration for its services as such Warrant Agent hereunder as set forth on Exhibit B hereto,
and will reimburse the Warrant Agent upon demand for all expenditures that the Warrant Agent may reasonably incur in the execution
of its duties hereunder.

 

7.3.2 Further Assurances. The Company agrees to perform,
execute, acknowledge, and deliver or cause to be performed, executed, acknowledged, and delivered all such further and other acts,
instruments, and assurances as may reasonably be required by the Warrant Agent for the carrying out or performing of the provisions
of this Warrant Agreement.

 

7.4    Liability of Warrant Agent.

 

7.4.1 Reliance on Company Statement. Whenever in the performance
of its duties under this Warrant Agreement, the Warrant Agent shall deem it necessary or desirable that any fact or matter be proved
or established by the Company prior to taking or suffering any action hereunder, such fact or matter (unless other evidence in
respect thereof be herein specifically prescribed) may be deemed to be conclusively proved and established by a statement signed
by the Chief Executive Officer, President, Chief Operating Officer, Chief Financial Officer, Executive Vice President, Secretary
or Assistant Secretary of the Company and delivered to the Warrant Agent. The Warrant Agent may rely upon such statement for any
action taken or suffered in good faith by it pursuant to the provisions of this Warrant Agreement.

 

7.4.2 Indemnity. The Warrant Agent shall be liable hereunder
only for its own gross negligence, willful misconduct or bad faith. The Company agrees to indemnify the Warrant Agent and save
it harmless against any and all liabilities, including judgments, costs and reasonable counsel fees, for anything done or omitted
by the Warrant Agent in the execution of this Warrant Agreement except as a result of the Warrant Agent's gross negligence, willful
misconduct, or bad faith.

 

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7.4.3 Exclusions. The Warrant Agent shall have no responsibility
with respect to the validity of this Warrant Agreement or with respect to the validity or execution of any Warrant (except its
countersignature thereof); nor shall it be responsible for any breach by the Company of any covenant or condition contained in
this Warrant Agreement or in any Warrant; nor shall it be responsible to make any adjustments required under the provisions of
Section 4 hereof or responsible for the manner, method, or amount of any such adjustment or the ascertaining of the existence of
facts that would require any such adjustment; nor shall it by any act hereunder be deemed to make any representation or warranty
as to the authorization or reservation of any shares of Common Stock to be issued pursuant to this Warrant Agreement or any Warrant
or as to whether any shares of Common Stock will when issued be valid and fully paid and nonassessable.

  

7.5    Acceptance of Agency. The Warrant Agent hereby accepts
the agency established by this Warrant Agreement and agrees to perform the same upon the terms and conditions herein set forth
and among other things, shall account promptly to the Company with respect to Warrants exercised and concurrently account for,
and pay to the Company, all moneys received by the Warrant Agent for the purchase of shares of the Company's Common Stock through
the exercise of Warrants.

 

7.6    Waiver. The Warrant Agent hereby waives any and all right,
title, interest or claim of any kind ("Claim") in or to any distribution of any account in which funds
related to the purchase or exercise of the Warrants are held, and hereby agrees not to seek recourse, reimbursement, payment or
satisfaction for any Claim against any such account for any reason whatsoever.

 

8.      Miscellaneous Provisions.

 

8.1    Successors. All the covenants and
provisions of this Warrant Agreement by or for the benefit of the Company or the Warrant Agent shall bind and inure to the benefit
of their respective successors and assigns.

 

8.2    Notices. Any notice or other communication required or
which may be given hereunder shall be in writing and either be delivered personally or by private national courier service, or
be mailed, certified or registered mail, return receipt requested, postage prepaid, and shall be deemed given when so delivered
personally or, if sent by private national courier service, on the next business day after delivery to the courier, or, if mailed,
two business days after the date of mailing, as follows:

 

Zion Oil & Gas, Inc.

6510 Abrams Road, Suite 300

Dallas, Texas 75231

Attn: Chief Executive Officer

 

Any notice, statement or demand authorized by this Warrant Agreement
to be given or made by the holder of any Warrant or by the Company to or on the Warrant Agent shall be sufficiently given when
so delivered if by hand or overnight delivery or if sent by certified mail or private courier service five days after deposit of
such notice, postage prepaid, addressed (until another address is filed in writing by the Warrant Agent with the Company), as follows:

 

American Stock Transfer & Trust Company, LLC

6201 15th Avenue

Brooklyn, New York 11219

Attn: Account Executive

 

    	8

    	 

    

 

8.3    Applicable Law. The validity, interpretation, and performance
of this Warrant Agreement and of the Warrants shall be governed in all respects by the laws of the State of New York, without giving
effect to conflict of laws. Each party hereby agrees that any action, proceeding or claim against it arising out of or relating
in any way to this Warrant Agreement shall be brought and enforced in the appropriate state or federal courts in the State of New
York, and irrevocably submits to such jurisdiction, which jurisdiction shall be exclusive. Each party hereby waives any objection
to such exclusive jurisdiction and that such courts represent an inconvenient forum.

 

8.4    Persons Having Rights under this Warrant Agreement. Nothing
in this Warrant Agreement expressed and nothing that may be implied from any of the provisions hereof is intended, or shall be
construed, to confer upon, or give to, any person or corporation other than the parties hereto and the registered holders of the
Warrants, any right, remedy, or claim under or by reason of this Warrant Agreement or of any covenant, condition, stipulation,
promise, or agreement hereof. All covenants, conditions, stipulations, promises, and agreements contained in this Warrant Agreement
shall be for the sole and exclusive benefit of the parties hereto and their successors and assigns and of the registered holders
of the Warrants.

 

8.5    Examination of the Warrant Agreement.
A copy of this Warrant Agreement shall be available at all reasonable times at the office of the Warrant Agent for inspection by
the registered holder of any Warrant. The Warrant Agent may require any such holder to submit his Warrant for inspection by it.

 

8.6    Counterparts. This Warrant Agreement may be executed
in any number of 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.

 

8.7    Effect of Headings. The Section headings herein are for
convenience only and are not part of this Warrant Agreement and shall not affect the interpretation thereof.

 

8.8    Amendments. This Warrant Agreement may be amended by
the parties hereto without the consent of any registered holder for the purpose of curing any ambiguity, or of curing, correcting
or supplementing any defective provision contained herein or adding or changing any other provisions with respect to matters or
questions arising under this Warrant Agreement as the parties may deem necessary or desirable and that the parties deem shall not
adversely affect the interest of the registered holders. All other modifications or amendments, including any amendment to increase
the Warrant Price or shorten the Exercise Period, shall require the written consent of a majority of the then outstanding Warrants.
Notwithstanding the foregoing, the Company may lower the Warrant Price or extend the duration of the Exercise Period in accordance
with Sections 3.1 and 3.2, respectively, without such consent.

 

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

 

    	9

    	 

    

 

IN WITNESS WHEREOF, this Warrant Agreement has been duly executed
by the parties hereto as of the day and year first above written.

 

	ZION OIL & GAS, INC.
	 
	By:	/s/ John M.
    Brown	 
	Name: 	John M. Brown	 
	Title:  	Chief Executive Officer	 
	 
	AMERICAN STOCK TRANSFER & TRUST COMPANY, LLC
	 
	By:	/s/ Michael A. Nespoli	 
	Name: 	Michael A. Nespoli	 
	Title:  	Executive Director	 

 

 

10

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