If any vacancy occurs in the membership of the board of trustees between the annual elections, the remaining members of the board may fill the vacancy by appointing a person with the required qualifications. The appointed person shall qualify in the same manner and hold office until the next annual election when a successor is elected. If all places on the board become vacant, then a new board shall be elected in the same manner as was the initial board.
SDCL 46A-10A-113