We were in Sicily last year and got rung up for expensive ZTL driving violations. We haven't been to Ireland since 1996. Do they have any ZTL type system in Ireland, including Northern Ireland?
There are no ZTL-like driving restrictions in any of the cities and towns in Ireland.
That said, the city centers (talking larger cities like Dublin, Cork, and Belfast) are such a rabbit warren of one-way streets, changing street names, often confusing signage and congestion that most here recommend not taking a car in there unless you're very familiar with the city layout and are comfortable with driving on the left.