The deceased person is a different entity from the estate. The estate needs a new PPSN of its own. You may need to be persistant.
I spent two years trying to get a PPS for my husband's estate. I went in person to the Revenue offices, I phoned, I wrote letters and emails to Revenue and Client Identity Services (who had provided a PPS for my UK aunt, no Irish connection, who had left me an inheritance), I sent messages from my own ROS account.
This February I finally received a PPSN for the estate, as a reply to my communication of August 2019, according to the accompanying letter.
Once you have the PPSN for the estate, follow instructions on Revenue.ie for ROS registration.
You will then be completing a Form 1 for Trusts and Estates.
While there is still income for the estate you will need to complete F1 for each relevant year.