Mo. Rev. Stat. § 77.450

If a vacancy occurs in any elective office other than the office of mayor, a successor to the vacant office shall be selected by appointment by the mayor with the advice and consent of a majority of the remaining members of the council. The council may adopt procedures to fill vacancies consistent with this section. The successor shall serve until the next available regular municipal April election. If a vacancy occurs in any office not elective, the mayor shall appoint a suitable person to discharge the duties of the same until the first regular meeting of the council thereafter, at which time the vacancy shall be permanently filled.