N.H. Rev. Stat. Ann. § 282-A:129

The term of office of each nonlegislative member of the advisory council shall be 3 years and until his successor is appointed and qualified. The term of office of each legislative member shall be coterminous with the legislative term. In the event of a vacancy in the membership of said council, the appointment shall be made in the manner provided in RSA 282-A:128 and for the unexpired term.