Consumes specifically targeted jokes on the radio (7)
I believe the answer is:
ingests
'consumes' is the definition.
('ingest' can be a synonym of 'consume')
'specifically targeted jokes on the radio' is the wordplay.
'specifically targeted' becomes 'in' (as in in-jokes, jokes to entertain a certain group).
'jokes' becomes 'jests' ('jest' can be a synonym of 'joke').
'on the radio' shows a homophone (sound like).
'jests' sounds like 'gests'.
'in'+'gests'='INGESTS'
(Other definitions for ingests that I've seen before include "Absorbs" , "Takes up" , "Swallows" .)