Mark has school backing (4)
I believe the answer is:
note
'mark' is the definition.
('note' can be a synonym of 'mark')
'school backing' is the wordplay.
'school' becomes 'eton' (famous UK public school).
'backing' is a reversal indicator.
'eton' written backwards gives 'NOTE'.
'has' acts as a link.
(Other definitions for note that I've seen before include "Pay attention to, tone" , "Eg, fiver; annotation" , "register" , "Musical tone" , "Crotchet or minim, perhaps" .)