In its final year, a trust can elect to have estimated tax paid treated as made by the beneficiaries (file Form 1041-T), but not tax withheld).
Regardless, if the trustee pays estimated tax from the trustee's personal funds, that would be considered to be a gift to the beneficiaries.
As @Critter-3 mentioned, professional guidance is highly recommended; the trustee is a fiduciary and is held to that standard of care.
