Finished with young lady in part of Ireland (7)
I believe the answer is:
donegal
'part of ireland' is the definition.
(I've seen this before)
'finished with young lady' is the wordplay.
'finished' becomes 'done' (both can mean completed).
'with' is a charade indicator (letters next to each other).
'young lady' becomes 'gal' (synonyms).
'done'+'gal'='DONEGAL'
'in' is the link.
(Other definitions for donegal that I've seen before include "County of NW?Ireland" , "town and county" , "County of NW Ireland" , "Ireland's northmost county" , "Lean dog (anag) - Irish county" .)