N.H. Rev. Stat. Ann. § 5:42

There is hereby established the state historical records advisory board composed of the state archivist who shall be chairman of the state historical records advisory board and at least 7 members to be appointed by the governor and council. The term of office for each of said appointed members shall be for 3 years. Each member shall hold office until his successor is appointed and qualified. In case of a vacancy other than by expiration of the term, the appointment shall be for the balance of the unexpired term.