Eat amusingly on the radio (6)
I believe the answer is:
ingest
'eat' is the definition.
(I've seen this before)
'amusingly on the radio' is the wordplay.
'amusingly' becomes 'injest' (something said in jest is intended to amuse).
'on the radio' indicates a 'sounds like' (homophone) clue.
'injest' sounds like 'INGEST'.
(Other definitions for ingest that I've seen before include "Take in with tinges" , "Eat - gin set (anag)" , "Absorb - signet (anag)" , "take in, eat" , "Take (food) into the body" .)