Mark turns up in a famous school (4)
I believe the answer is:
eton
'a famous school' is the definition.
(English private school)
'mark turns up' is the wordplay.
'mark' becomes 'note' (mark can mean to note or remember).
'turns up' says the letters should be written in reverse.
'note' back-to-front is 'ETON'.
'in' is the link.
(Other definitions for eton that I've seen before include "Note sent up to English public school" , "School - note (anag)" , "Leading English public school" , "Kind of collar or jacket (worn at college?)" , "collar, perhaps?" .)