Trustees are personally liable for the tax obligations of the trust.
If a trustee resigns as trustee of a trust they must let IRD know in writing, as soon as possible following the resignation, so IRD can update their records.
Related reading: Resigning as a NZ trustee
If a trustee resigns and doesn't let IRD know, they'll still recognise them as a trustee which makes them liable for any tax obligations of the trust. IRD will continue to recognise them as a trustee until written confirmation is received.
For income tax and GST purposes, a trustee may be liable for any outstanding tax for the periods they were a trustee. This includes the period of time between their resignation and IRD receiving confirmation of the resignation. This liability continues until the debt is paid.