In general, trusts are not designed to have power of attorneys. Instead, a successor trustee is generally designated in the trust to manage the trust if the original trustee resigns, becomes incapacitated, or becomes deceased.
In rare situations, trusts do allow for a power of attorney. In such cases, the trust would specifically allow the trustee to appoint an attorney in fact and the trustee’s power of attorney document would specifically allow the attorney in fact to manage the trust.