S.C. Code Ann. § 62-7-705
Unless otherwise provided in the trust instrument, while continuing to act as a trustee, the trustee may not transfer his office to another or delegate the entire administration of the trust to a co-trustee or another. The trustee may resign if:
(3) the court approves the resignation.
A beneficiary may consent if the beneficiary is not a minor or incapacitated person or the resignation is consented to by the representative of the minor or incapacitated person as described in Section 61-1-403(1) and (2).