Irish county finished off tune we hear (7)
I believe the answer is:
kildare
'irish county' is the definition.
(I know that Kildare is a county of Ireland)
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for kildare that I've seen before include "doctor from long ago" , "division in Ireland" , "Irish county near Dublin" , "part of Ireland" , "County of Ireland" .)