Does a prior-year zero-tax Form 1041 avoid estimated tax penalty?

Yes, it can. Current Form 2210 instructions include an exception when there was no prior-year tax liability, the taxpayer met the required status condition, and the prior-year return was or would have been for a full 12 months. For a domestic trust, that prior-year full-period no-tax fact can be the reason no underpayment penalty applies.

The words "full 12 months" matter. A short-year fiduciary return or a missing prior-year return can change the result. For an EA-style notice response, attach or reference the prior-year Form 1041, show that the tax liability was zero, and explain the full-year condition.