Yes, if you are already named as the successor trustee, they can do this: all they need to do is to draft and sign a document stating that they resign as and going forward refuse to serve as trustee. The document shoud be witnessed and notarized the same way the documents creating the trust in the first place were witnessed and notarized when the trust was set up (i.e. follow the same formalities). If the trust documents require that a named trustee do anything when resigning, also do whatever this trust requires.