Michael, the above suggestions are all excellent, and I would definitely agree that the Doolin
Folk Festival is one of the musical highlights in County Clare during the summer months! :)
However, if you are interested in experiencing something a little bit different, you could also check out the Doonbeg
International Jazz Festival, which also takes place in June. This festival welcomes talented musicians from all over the world, and when you combine this with the charming Irish “craic” culture, it makes for one unique festival!
Clare is widely considered to be the traditional music capital
of Ireland and, as Eoin mentioned, you will have no problem finding a “seisún” to join in on while you're in Ennis! These are often spontaneous affairs, but if you wish, you can keep an eye on upcoming sessions here
Ireland has a fantastic festival scene, catering to not only music fans, but film buffs, foodies and lovers of literature; You can find out more about Irish festivals by taking a look at this article.
I hope this helps you plan your trip, Michael! If you need any other suggestions, just let me know! :D