Reportedly regretted being cross (4)
I believe the answer is:
rood
'being cross' is the definition.
(term for a crucifix)
'reportedly regretted' is the wordplay.
'reportedly' indicates a 'sounds like' (homophone) clue.
'regretted' becomes 'rued' ('rue' can be a synonym of 'regret').
'rued' sounds like 'ROOD'.
(Other definitions for rood that I've seen before include "Cross, crucifix" , "Old land measure and large cross in a church" , "Crucifix in entrance, set back" , "Crucifix on door" , "Old land measure of quarter of an acre" .)