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