Record where Boris was rejected (4)
I believe the answer is:
note
'record' is the definition.
(note is a kind of record)
'where boris was rejected' is the wordplay.
'where boris was' becomes 'eton' (Boris Johnson's old school).
'rejected' is a reversal indicator.
'eton' reversed gives 'NOTE'.
(Other definitions for note that I've seen before include "Short message; tone" , "Short message; piano key" , "Jotting" , "Cash" , "Musical tone" .)