When the grant of probate issues your (I assume you are a sole executor) responsibilities are to gather in what is owed
to the estate (the assets) and to discharge what is owed
by the estate (the liabilities). The grant of probate gives you the legal authority to deal with these matters. Practically speaking some matters can be dealt with in advance. e.g. I paid for my mother's funeral and recovered the costs from the estate when probate issued.
It is an essentially pedantic exercise in that you list out everything to be recovered and discharged. You can start writing up your lists now so that you are ready to go when probate issues.
In your case it might be helpful to open an executor's account with your bank to facilitate moving money in and out as you deal with the estate. I did a personal probate also but found some financial institutions a bit messy and sticky in terms of the payee on cheques when I was collecting in the assets
.
In relation to both of my parents they were on PAYE. After probate issued, I simply completed income tax returns for both of them to complete and close their tax affairs. There were refunds in each case.
Your mother was in a nursing home. There may be very valuable tax rebates due for the nursing home fees
apart from any Fair Deal considerations if they apply. Revenue will have the information you need on that.
There may be capital taxes payable on inheritances. As far as I remember they are effectively self declaration taxes. When probate issues Revenue will receive a copy (from the Probate Office) of the CA24 that you completed for the probate application. Beneficiaries may well receive a notice from Revenue asking them to complete a return. I think that the trigger for a return is if the benefit received reaches 80% of the relevant CAT threshold.
Don't forget that this will apply to you too if you are also a beneficiary.
Some of this can be a bit overwhelming. If so, do not be afraid to consult a solicitor or an accountant for help. I had a slightly complicated tax wrinkle on an inheritance but the €350 I spent on an accountant to resolve it was very well worth the money and peace of mind.
Working principle for probate : Keep calm but carry on promptly as penalties can accrue if certain things are delayed.