Short letter turning up in school (4)
I believe the answer is:
eton
'school' is the definition.
(famous UK public school)
'short letter turning up' is the wordplay.
'short letter' becomes 'note' (synonyms).
'turning up' shows that the letters should be reversed in order.
'note' backwards is 'ETON'.
'in' is the link.
(Other definitions for eton that I've seen before include "collar, perhaps?" , "old school" , "Berkshire town" , "School - note (anag)" , "Town on the Thames noted for its school" .)