Set up public school for me? (4)
I believe the answer is:
note
'me?' is the definition.
(I've seen this before)
'set up public school' is the wordplay.
'set up' says the letters should be written in reverse (in a down clue, letters go up).
'public school' becomes 'eton' (Eton College).
'eton' backwards is 'NOTE'.
'for' is the link.
(Other definitions for note that I've seen before include "Short communication" , "Short message; tone" , "Record; memo" , "Reminder - fame - sound" , "Eg, fiver; annotation" .)