Observe public school is on the way up (4)
I believe the answer is:
note
'observe' is the definition.
('note' can be a synonym of 'observe')
'public school is on the way up' is the wordplay.
'public school' becomes 'eton' (I've seen this before).
'is on the way up' says the letters should be written backwards.
'eton' written backwards gives 'NOTE'.
(Other definitions for note that I've seen before include "Mark - sound - money" , "Put down" , "Pay attention to; record" , "Consequence" , "Tone of a short record" .)