Idaho Code § 42-2912: Vacancies.

In case a vacancy or vacancies occur in said board by death, failure to appoint, failure to qualify, or resignation of one or more of the members thereof, such vacancy or vacancies shall be filled at once by appointment by the judge of the district court of the county in which said district is located, and said appointee shall serve for the unexpired term, or until his successor is appointed and his bond approved.