The only popular Irish Women musicians I know of are:

Enya , Maire Brennan , Molly McGuire , Loreena McKennitt , Sinead O'Connor , and Dolores O'Riordan from the Cranberries.

You may be thinking Tori Amos , who plays piano , but I dont think she was born in Ireland. But her flamming red hair would certainly suggest its in her blood.