Mark turned up for school (4)
I believe the answer is:
eton
'school' is the definition.
(famous UK public school)
'mark turned up' is the wordplay.
'mark' becomes 'note' ('note' can be a synonym of 'mark').
'turned up' says the letters should be written in reverse.
'note' reversed gives 'ETON'.
'for' is the link.
(Other definitions for eton that I've seen before include "Posh college" , "old school" , "British public school of note" , "Berkshire public school" , "Famous English public school" .)