Bird used wings, heading off after dog (6)
I believe the answer is:
curlew
'bird' is the definition.
(curlew is a kind of bird)
'used wings heading off after dog' is the wordplay.
'used wings' becomes 'flew'.
'heading off' means to remove the first letter.
'after' says to put letters next to each other.
'dog' becomes 'cur' (cur is a kind of dog).
'flew' with its initial letter taken off is 'lew'.
'lew' after 'cur' is 'CURLEW'.
(Other definitions for curlew that I've seen before include "Bird with long down-curved bill" , "Large shorebird" , "Curve-beaked bird" , "Moorland bird" , "Wader with downcurved bill" .)