If the electors of a township fail to elect the proper number of officers, or a person elected to a township office fails to qualify, or a vacancy happens in any such office from death, resignation, removal from the township, or other cause, the board of township supervisors, or a majority of them, shall fill the vacancy by appointment, and the person so appointed shall hold that office until the next annual meeting and until the person's successor is elected and qualified.
N.D.C.C. § 58-05-16