When 2 or more townships are united into one, or when a township is divided into 2 or more townships, a new election shall be ordered in the new township or townships by the county board and held at the time scheduled under the general election law for the holding of township elections. The election shall be conducted in the manner prescribed by the general election law. When parts of several townships are taken to make a new township, an election need not be ordered in the townships from which territory is taken. If, however, any officer of one of those townships continues to reside in the new township, his or her office shall be declared vacant and filled as in other cases of vacancy.