Girl gets one in the finish (4)
I believe the answer is:
enid
'girl' is the definition.
(girl's name)
'one in the finish' is the wordplay.
'one' becomes 'i' (Roman numeral).
'in' is an insertion indicator.
'the finish' becomes 'end' (I've seen this in other clues).
'i' placed into 'end' is 'ENID'.
'gets' is the link.
(Other definitions for enid that I've seen before include "- Blyton, children's writer" , "Geraint's loved one" , "'... Blyton, children's author (4)'" , "- Blyton, twentith century writer" , "Woman" .)