In short: Yes! The trust deed sets out the scope of a trustee’s powers. So, if you have specific requirements, consider drafting a deed to limit, constrain or manage their powers. Trustees are also subject to a variety of other requirements from both common law and statute.
Notably, a trustee has a fiduciary relationship with the beneficiaries. This relationship exists because of the trust placed in the trustee. To protect those in a vulnerable position (those putting trust in the trustee), the law recognises this special relationship and places duties on the trustee to ensure they act in good faith and the trust’s best interests.