Husband's left part of church, getting cross out (6)
I believe the answer is:
cancel
'cross out' is the definition.
'husband's left part of church' is the wordplay.
'husband' becomes 'h'.
'left' suggests deleting specific letters.
'part of church' becomes 'chancel' ('chancel' is part of 'church').
'chancel' with 'h' removed is 'CANCEL'.
'getting' is the link.
(Other definitions for cancel that I've seen before include "Rescind, abolish" , "Go for an annulment" , "Strike out" , "Call off (arranged event)" , "stop?" .)