N.D. Cent. Code § 40-04.1-03

If a vacancy occurs in the office of councilman by death, resignation, or otherwise, the city may call a special election to fill such vacancy for the unexpired term or may after fifteen days of the date of such vacancy appoint a person from the ward or city at large by which the councilman previously holding was elected or appointed to fill such vacancy until the next city election, at which election the unexpired term shall be filled.