Register from school written up (4)
I believe the answer is:
note
'register' is the definition.
(register can mean to note or observe)
'school written up' is the wordplay.
'school' becomes 'eton' (famous UK public school).
'written up' says the letters should be written in reverse (in a down clues, letters go up).
'eton' in reverse letter order is 'NOTE'.
'from' is the link.
(Other definitions for note that I've seen before include "A, B, C, D, F or G" , "Eg, minim" , "Put down" , "mention" , "Single tone; short letter" .)