Regretted offensive broadcast (4)
I believe the answer is:
rued
'regretted' is the definition.
('rue' can be a synonym of 'regret')
'offensive broadcast' is the wordplay.
'offensive' becomes 'rude'.
'broadcast' indicates a 'sounds like' (homophone) clue (how the word might sound on the radio or TV).
'rude' sounds like 'RUED'.
(Other definitions for rued that I've seen before include "Was contrite about" , "Was sorry" , "'Regretted, repented (4)'" , "Bitterly regretted" , "was remorseful" .)