Woman rejected current husband, getting together with Harry Barker (5,9)
I believe the answer is:
irish wolfhound
'barker' is the definition.
(breed of dog - something which barks)
'woman rejected current husband getting together with harry' is the wordplay.
'woman' becomes 'Iris' (woman's name).
'rejected current husband' becomes 'hwolf' (I can't justify this - if you can you should believe this answer much more).
'getting together with' says to put letters next to each other.
'harry' becomes 'hound' (both can mean to harass).
'iris'+'hwolf'+'hound'='IRISH WOLFHOUND'
(Other definitions for irish wolfhound that I've seen before include "Barker?" , "Shown [AT CRUFTS]" .)