Mo. Rev. Stat. § 82.040

All persons in office in such city at the time of the ratification of such charter shall hold their offices until their successors are elected or appointed and qualified, as may be provided in such charter, but no longer. At any time there is a vacancy in any office in a city not within a county, where a person is to be appointed by the governor to fill such vacancy, the deputy officer for that particular office shall serve in the interim until such appointment is made.