N.H. Rev. Stat. Ann. § 547:18

Whenever there is a vacancy in the office of the judge of probate of any county, the administrative judge of the probate court shall call upon the judge of some other county, who shall act during such vacancy. Such judge who is called upon shall receive the same per diem compensation determined by the supreme court upon recommendation by the judicial branch administrative council, plus reasonable expenses, which shall be paid by the state.