Graduates quickly finding instrument (7)
I believe the answer is:
bassoon
'instrument' is the definition.
(type of musical instrument)
'graduates quickly' is the wordplay.
'graduates' becomes 'BAs' (people with Bachelor of Arts degrees).
'quickly' becomes 'soon' (I've seen this in other clues).
'bas'+'soon'='BASSOON'
'finding' is the link.
(Other definitions for bassoon that I've seen before include "Instrument - no ASBOs (anag)" , "Tenor of the oboe family" , "Hollow instrument" , "Instrument heard by Wedding-Guest" , "It is played" .)