Mo. Rev. Stat. § 115.617: Vacancy, how filled.

Whenever a member of any county or city committee dies, resigns, or ceases to be a registered voter of or a resident of the county or a city not within a county or the committee district from which he is elected, a vacancy shall exist on the committee. A majority of the committee shall elect another person to fill the vacancy who, for one year next before his election, shall have been both a registered voter of and a resident of the county or city and the committee district. The person selected to fill the vacancy shall serve the remainder of the vacated term.