S.D. Codified Laws § 21-22-12
In case of the vacancy of the office of trustee, unless the instrument creating the trust names the successor, or allows the resigning trustee or another person to appoint its successor, the successor shall be appointed by the court upon hearing and notice as provided in this chapter. In case of necessity the court may appoint a temporary trustee pending a permanent appointment.
If the office of trustee remains vacant for more than thirty days, then any resigned trustee in possession of trust property may petition the court for the appointment of a successor trustee. If no successor trustee can be secured within ninety days following a hearing held of the resigned trustee's petition, the resigned trustee shall deliver the trust property within its possession to any other fiduciary or other persons, as ordered by the court.
The resigned trustee shall be held harmless from any liability, absent the resigned trustee's gross negligence or willful misconduct, for any action taken pursuant to this section.
The resigned trustee is entitled to reimbursement for advances it has made on behalf of the trust and for reasonable compensation for the performance of its duties as trustee. Such advances and compensation shall act as a lien on trust assets under § 55-1A-34.
Following a trustee's resignation, the resigned trustee shall be deemed to be serving only as a custodian of the documents and assets of the trust then in its possession and shall be relieved of its fiduciary and administrative duties under the terms of the trust instrument and pursuant to state law. The resigned trustee is entitled to reimbursement for advances it has made on behalf of the trust and for reasonable compensation as a custodian. Such advances and compensation shall act as a lien on trust assets under § 55-1A-34.
The relief afforded to the trustee under this section does not limit other relief that may be requested or authorized under this chapter.
SDCL 21-22-12