S.D. Codified Laws § 3-4-11
If any position on a board or commission whose members are appointed by the Governor with the consent of the Senate becomes vacant pursuant to § 3-4-1, the Governor may make an interim appointment to fill the vacancy, but any interim appointment expires when the Senate acts upon the appointee's nomination. If the vacancy is the result of a resignation, the person who has resigned remains on the board or commission until the Governor appoints a person with the consent of the Senate or makes an interim appointment to fill the vacancy or until a date set in writing by the person who resigned, whichever is sooner.
If a person's term on the board or commission has expired, the person remains on the board or commission until the Senate consents to the appointment of the Governor's nominee or until the Senate acts upon the renomination of the person whose term has expired. If the Governor does not nominate a person for the new term by the tenth legislative day after the Legislature convenes, the person whose term has expired is deemed to be renominated for the new term and the Senate may act on the nomination accordingly. If a person is unable to serve an additional term due to a term limit, the person is not deemed renominated pursuant to this section and may not remain on the board or commission pursuant to this section after the adjournment of the next legislative session after the person's term expires.
This section applies to any board or commission whose members are appointed by the Governor with the consent of the Senate unless the board or commission is specifically exempted from this section by law.
SDCL 3-4-11