Mutton graduate gives girl (4)
I believe the answer is:
emma
'girl' is the definition.
'mutton graduate' is the wordplay.
'mutton' becomes 'em' (synonyms).
'graduate' becomes 'ma' (abbreviation for Master of Arts).
'em'+'ma'='EMMA'
'gives' acts as a link.
(Other definitions for emma that I've seen before include "Jane Austen work - Ms Bunton, former Baby Spice" , "Jane Austen heroine" , "book" , "novelist's work" , "young woman in novel" .)