Mo. Rev. Stat. § 190.052
Any member of the board of directors who moves residency from the district from which the member was elected shall be disqualified as a member of the board. If one or two vacancies occur in the membership of the board as a result of death, resignation, or disqualification, the remaining members shall appoint one or two qualified persons, as provided in section 190.050, to fill the vacancies until the end of the unexpired term. Such appointment shall be made with the consent of a majority of the remaining members of the board. If the board is unable to agree in filling a vacancy within sixty days or if there are more than two vacancies at any one time, the county commission, upon notice from the board of failure to agree in filling the vacancies, shall within ten days fill them by appointment of qualified persons, as provided in section 190.050, and shall notify the persons in writing of their appointment. The persons appointed shall serve for the unexpired term.
§ 190.052, RSMo