N.M. Stat. § 19-10-47
When any such agreement has been approved by the commissioner, he may, with the approval of the lessee evidenced by the lessee's execution of such agreement or otherwise, amend any oil or gas lease embracing state lands within the area included in such agreement so that the provisions of such lease so far as they apply to lands within such area will conform to the provisions of such agreement and so that the length of the secondary term as to lands within such area will be extended, insofar as necessary, to coincide with the term of such agreement, and the approval of such agreement by the commissioner and the lessee, as aforesaid, shall without further action of the commissioner or the lessee be effective to conform the provisions and extend the term of such lease as to lands within such area, to the provisions and terms of such agreement; or the commissioner may permit the holder of any such lease of state lands within such area to surrender such lease, so far as it embraces lands within such area, with the preference right to a new lease for the lands surrendered, containing such provisions and for such a term as will conform to the provisions and term of such agreement. The commissioner is authorized to issue such new lease under regulations prescribed by him. No law applicable to restricted districts and the making of oil and gas leases therein, or providing for a minimum rental within restricted districts, shall be applicable to any lease conformed or issued hereunder.
If any such agreement provides for extensions of the term thereof, any such extension pursuant to the provisions of such agreement shall, with the approval of the commissioner, be effective also to extend the term of such lease, so far as it applies to lands within such area, to coincide with the extended term of such agreement.
NMS § 19-10-47