Bit of an eye for a girl (4)
I believe the answer is:
iris
I believe this is a double definition.
'bit of an eye' is the first definition.
('iris' is part of 'eye')
'a girl' is the second definition.
'for' acts as a link.
(Other definitions for iris that I've seen before include "In the middle of which pupil is opening" , "Flower - rainbow" , "Eye part or attractive flower" , "Nice flower or eye part" , "Flag,flower and part of the eye" .)