Big cat identified by quiet university graduate (4)
I believe the answer is:
puma
'big cat' is the definition.
(I've seen this before)
'quiet university graduate' is the wordplay.
'quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'university' becomes 'U' (abbreviation as in UMass).
'graduate' becomes 'MA' (abbreviation for Master of Arts).
'p'+'u'+'ma'='PUMA'
'identified by' is the link.
(Other definitions for puma that I've seen before include "Big cat" , "US wild cat" , "South American carnivore" , "Large wild American feline" , "Large Am. wild cat" .)