Mo. Rev. Stat. § 79.280
If a vacancy occurs in any elective office, the mayor or the person exercising the duties of the mayor shall cause a special meeting of the board of aldermen to convene where 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 board of aldermen. If the vacancy is in the office of mayor, nominations of a successor may be made by any member of the board of aldermen and selected with the consent of a majority of the members of the board of aldermen. The board of aldermen may adopt procedures to fill vacancies consistent with this section. The successor shall serve until the next regular municipal election. If a vacancy occurs in any office not elective, the mayor shall appoint a suitable person to discharge the duties of such office until the first regular meeting of the board of aldermen thereafter, at which time such vacancy shall be permanently filled.
§ 79.280, RSMo