There are several music festivals in county clare over the summer period but dates for 2017 events won't be confirmed probably at this point. The west coast towns of miltown malbay, lahinch, kilrush, kilkee, lisdoonvarna and doonbeg are the main locations for the most popular events and each year the dates will vary slightly so you'll need to check in late 2016 or early 2017 for the exact dates.
In June the main event is the Doolin Music Festival - http://www.doolinfolkfestival.com
The biggest traditional music festival in County Clare is the Willie Clancy Festival but this actually starts usually on the first weekend of July and runs for 10 days - http://www.scoilsamhraidhwillieclancy.com/
In the summer months you'll not have to look very far in any town in County Clare to find live music in pubs & bars and other venues like community halls. The county town of Ennis is actually located 20 minutes from Shannon Airport and about 30 - 50 minutes drive from most of the coastal towns referred to above. In Ennis there is a Music festival at the end of May called the Fleadh Nua which might be of interest if you've coming a little earlier - http://www.fleadhnua.com