Relieved idiot carried on broadcast (8)
I believe the answer is:
assuaged
'relieved' is the definition.
('assuage' can be a synonym of 'relieve')
'idiot carried on broadcast' is the wordplay.
I cannot quite understand how this works, but
'idiot' could be 'ass' (both can mean a stupid person) and 'ass' is found in the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for assuaged that I've seen before include "Allayed, alleviated" , "made less strong" , "Alleviated, pacified" , "Slaked, satisfied" , "mollified" .)