S.D. Codified Laws § 46A-3B-9
Each director shall take office on the first day of January of the year following election, or not later than sixty days after election in the case of a special election. A vacancy that may occur on the water development district board of directors by reason of death, failure to be a resident and voter, resignation, or other cause pursuant to § 3-4-1, or upon expiration of term of office if no qualifying petitions have been filed or if no successor has qualified for the office, unless otherwise provided in chapters 46A-3A to 46A-3E, inclusive, shall be declared to exist and shall be filled by elective action of the remaining directors from candidates proposed by nominating petitions signed by at least twenty-five eligible voters in the director area for which a vacancy exists. The person appointed to fill the vacancy shall serve for the remainder of the unexpired term.
SDCL 46A-3B-9