Ceremony proper, on the radio (4)
I believe the answer is:
rite
'ceremony' is the definition.
(I know that rite is a type of religious ceremony)
'proper on the radio' is the wordplay.
'proper' becomes 'right' (similar in meaning).
'on the radio' indicates a 'sounds like' (homophone) clue.
'right' is a homophone of 'RITE'.
(Other definitions for rite that I've seen before include "Uncomplaining person" , "something like mass" , "Formal procedure" , "Tire of ceremony" , "(Words used in) ceremonial" .)