Prestige of school raised (4)
I believe the answer is:
note
'prestige' is the definition.
(someone 'of note' has prestige)
'school raised' is the wordplay.
'school' becomes 'eton' (famous UK public school).
'raised' says the letters should be written backwards (going up in a down clue).
'eton' written backwards gives 'NOTE'.
'of' is the link.
(Other definitions for note that I've seen before include "Brief letter - distinction" , "Pay attention to, tone" , "Record; memo" , "It could be me" , "Characteristic" .)