The governor appoints justices, who must be confirmed by the New Hampshire Executive Council, the five members of which are chosen biannually in partisan elections. Since 2000, the governor typically establishes a commission by executive order to screen and recommend candidates for the appointment. Confirmed justices serve on the court until the age of 70.
Selection method sources:
Ballotpedia, Judicial Election Methods By State; Brennan Center for Justice, Judicial Selection: An Interactive Map