N.H. Rev. Stat. Ann. § 330-A:8

The governor and council may remove any member of the board for misconduct, incompetence, neglect of duty, or other sufficient cause after the member has been given a written statement of the charges and an opportunity to be heard regarding such charges. Any vacancy in the membership of the board occurring otherwise than by expiration of a member's term shall be promptly filled for the unexpired term.