Living single after former wife? Smart! (8)
I believe the answer is:
existing
'living' is the definition.
('exist' can be a synonym of 'live')
'single after former wife? smart' is the wordplay.
'single' becomes 'i' (one).
'after' means one lot of letters go next to another.
'former wife?' becomes 'ex'.
'smart' becomes 'sting' (stinging is a kind of smarting**).
'i' after 'ex' is 'exi'.
'exi'+'sting'='EXISTING'
(Other definitions for existing that I've seen before include "Extant, alive" , "Surviving" , "Currently living" , "Having place as part of reality" , "To be found in the real world" .)