S.D. Codified Laws § 55-16-6

If a qualified person of a trust ceases to meet the requirements of § 55-16-3, and there remains no trustee that meets such requirements, such qualified person shall be deemed to have resigned as of the time of such cessation, and thereupon the successor qualified person provided for in the trust instrument shall become a qualified person of the trust, or in the absence of any successor qualified person provided for in the trust instrument, the circuit court shall, upon application of any interested party, appoint a successor qualified person.