Wyo. Stat. Ann. § 17-10-218

If a patron member director's position becomes vacant for a director that was elected by patron members, the board shall appoint a patron member of the cooperative to fill the director's position until the next regular or special members' meeting. If the vacating director was not a patron member, the board shall appoint a patron member to fill the vacant position. At the next regular or special members' meeting, the members or patron members shall elect a director to fill the unexpired term of the vacant director's position.