Advance quietly in university class (7)
I believe the answer is:
upgrade
'advance' is the definition.
(I've seen this before)
'quietly in university class' is the wordplay.
'quietly' becomes 'p' (p for piano and quiet).
'in' indicates putting letters inside.
'university' becomes 'u'.
'class' becomes 'grade' (grading is a kind of classing**).
'u'+'grade'='ugrade'
'p' going into 'ugrade' is 'UPGRADE'.
(Other definitions for upgrade that I've seen before include "promotion" , "Improvement" , "Higher-standard version" , "Improve equipment or promote" , "Raise to higher standard" .)