Country lady needing no introduction (4)
I believe the answer is:
oman
'country' is the definition.
(Oman is an example)
'lady needing no introduction' is the wordplay.
'lady' becomes 'woman' (I've seen this before).
'needing no introduction' means to remove the first letter.
'woman' with its first letter taken off is 'OMAN'.
(Other definitions for oman that I've seen before include "Middle Eastern country" , "Gulf sultanate" , "Arab country" , "Sultanate in southwest Asia" , "Sultanate, capital Muscat" .)