I believe there are currently access restrictions on Pol Elva, though the Polnagollum? systems is still accessible.
Pol an Ionenen is now a showcave. They've made a massive staircase/walkway through what used to be the cavers enterance.
St. Catherine's is check at the farm enterance for politeness.
All the other major Claire systems were just turn up and cave as of my last visit there, 2 years ago.
Depending on how long you are in Clare - try and get to:
Doolin river cave - Catherine's to Arran View is a lovely through trip
Polnagolum - shame about PolElva, because this was another ace through trip, now you can only explore form one end.
Cullum 2 and 5
Pol Dubh? / Coolaugh River cave - can be a through trip - long and route finding is tricky. VERY weather dependant!
Then there is various shorter stuff that is also enjoyable
Poulnagree being a personal choice.
I've no idea what the rest of the Irish caving scene is like?