Bird dog heading off (5)
I believe the answer is:
eagle
'bird' is the definition.
(eagle is a kind of bird)
'dog heading off' is the wordplay.
'dog' becomes 'beagle' (beagle is a kind of dog).
'heading off' means to remove the first letter.
'beagle' with its first letter taken away is 'EAGLE'.
(Other definitions for eagle that I've seen before include "somewhat under par" , "Bird with hooked bill and long broad wings" , "standard for the military is seen" , "Coin made of gold" , "Two under in 20 across" .)