College polished off, we hear? (4)
I believe the answer is:
eton
'college' is the definition.
(Eton College, English private school)
'polished off we hear?' is the wordplay.
'polished off' becomes 'eaten' (I've seen this in another clue).
'we hear?' indicates a 'sounds like' (homophone) clue.
'eaten' sounds like 'ETON'.
(Other definitions for eton that I've seen before include "Town opposite Windsor on the Thames" , "Public school, established in 1440" , "Berkshire public school" , "Posh British public school" , "Town on the Thames noted for its school" .)