Dog we left to run back for bird (6)
I believe the answer is:
curlew
'for bird' is the definition.
(curlew is a kind of bird)
'dog we left to run back' is the wordplay.
'dog' becomes 'cur' (both can mean a despicable person).
'left' becomes 'l' (common abbreviation).
'to run back' shows that the letters should be reversed in order (I've seen 'running back' mean this).
'we'+'l'='wel'
'wel' backwards is 'lew'.
'cur'+'lew'='CURLEW'
(Other definitions for curlew that I've seen before include "Flyer" , "Large wading bird" , "Shorebird with long down-curved bills" , "Bird with long down-curved bill" , "Wading bird with long down-curved beak" .)