The Revenue should be advised that he died - but, to be frank, it's not something that needs to be at the top of the list of things to deal with. They are used to this sort of situation, and will co-operate in trying to get any tax liability regularised.
If there is a will, an executor should deal with things; if there is no will, an administator will be responsible. The appointment of an executor or administrator is done by the Probate Office, as an agent of the court (obviously, people need to apply to be appointed).
Tax liability does not disappear when the taxpayer dies. But the Revenue are reasonable people and try to be helpful, so it should be possible to work out a settlement, even if there is an element of estimation.