N.H. Rev. Stat. Ann. § 661:9-a

If a vacancy occurs in the office of register of probate, the probate court shall appoint a commissioner to fill the vacancy for the unexpired term. If any register of probate becomes temporarily absent or incapacitated, the probate court may, in its discretion, declare a temporary absence and fill the same for a limited period of time, but in any event, not to exceed the unexpired term.