Leaving former wife single can start to grate (7)
I believe the answer is:
exiting
'leaving' is the definition.
('exit' can be a synonym of 'leave')
'former wife single can start to grate' is the wordplay.
'former wife' becomes 'ex'.
'single' becomes 'i' (one).
'can' becomes 'tin' ('tin' can be a synonym of 'can').
'start to' says to take the initial letters.
The first letter of 'grate' is 'g'.
'ex'+'i'+'tin'+'g'='EXITING'
(Other definitions for exiting that I've seen before include "Going out" , "Leaving" .)