N.H. Rev. Stat. Ann. § 4:4

In cases where the terms of office of the members of any permanent state board, commission or committee do not expire in successive years, the governor, with the advice and consent of the council may in making any appointment or filling any vacancy to such office, appoint any person for a period less than the full term in order to adjust the commissions of each member so that their terms of office will expire in successive years.