Not exactly a part for a girl (6)
I believe the answer is:
carole
'a girl' is the definition.
(girl's name)
'not exactly a part' is the wordplay.
'not exactly' becomes 'ca' (circa).
'a part' becomes 'role' (eg a theatrical role).
'ca'+'role'='CAROLE'
'for' acts as a link.
(Other definitions for carole that I've seen before include "- Lombard, US actress" , "girl" , "<196> - King, US singer" .)