Keen to embrace that female in bright red (6)
I believe the answer is:
cherry
'bright red' is the definition.
(I've seen this before)
'keen to embrace that female' is the wordplay.
'keen' becomes 'cry' (I've seen this in other clues).
'to embrace' is an insertion indicator.
'that female' becomes 'her' (I've seen this before).
'cry' placed around 'her' is 'CHERRY'.
'in' is the link.
(Other definitions for cherry that I've seen before include "new ball?" , "Morello-flavoured liqueur" , "Tree; red fruit" , "Bright red" , "Cerise" .)