Loudly regretted getting cross (4)
I believe the answer is:
rood
'cross' is the definition.
(term for a crucifix)
'loudly regretted' is the wordplay.
'loudly' indicates a 'sounds like' (homophone) clue.
'regretted' becomes 'rued' ('rue' can be a synonym of 'regret').
'rued' sounds like 'ROOD'.
'getting' is the link.
(Other definitions for rood that I've seen before include "Pole, perch or crucifix" , "Area equal to 40 square rods" , "old piece of land" , "Crucifix in entrance, set back" , "Crucifix; old land area measure" .)