Cross and offensive, by the sound of it (4)
I believe the answer is:
rood
'cross' is the definition.
(rood is a kind of cross)
'offensive by the sound of it' is the wordplay.
'offensive' becomes 'rude'.
'by the sound of it' shows a homophone (sound like).
'rude' sounds like 'ROOD'.
'and' is the link.
(Other definitions for rood that I've seen before include "Crucifix on door" , "old piece of land" , "Crucifix in church; one quarter of an acre" , "The Holy . . . . was the Cross of Christ" , "Old land measure and large cross in a church" .)