Mark is back in a famous school (4)
I believe the answer is:
eton
'a famous school' is the definition.
(English private school)
'mark is back' is the wordplay.
'mark' becomes 'note' (mark can mean to note or remember).
'is back' is a reversal indicator.
'note' written backwards gives 'ETON'.
'in' acts as a link.
(Other definitions for eton that I've seen before include "Kind of collar or jacket (worn at college?)" , "Posh English school of note" , "Berkshire public school" , "Collar - crop - jacket - school" , "Public school founded in 1440" .)