Regretted being offensive on the radio (4)
I believe the answer is:
rued
'regretted' is the definition.
(I've seen this before)
'offensive on the radio' is the wordplay.
'offensive' becomes 'rude'.
'on the radio' shows a homophone (sound like).
'rude' is a homophone of 'RUED'.
'being' is the link.
(Other definitions for rued that I've seen before include "Was contrite about" , "was remorseful" , "Was sorry" , "'Regretted, repented (4)'" , "Bitterly regretted" .)