Bird of prey heading off hunting dog (5)
I believe the answer is:
eagle
'bird of prey' is the definition.
(eagle is a kind of bird of prey)
'heading off hunting dog' is the wordplay.
'heading off' means to remove the first letter.
'hunting dog' becomes 'beagle' (beagle is a kind of hunting dog).
'beagle' with its first letter removed is 'EAGLE'.
(Other definitions for eagle that I've seen before include "The emblem of the US is bald" , "King of birds" , "experts are putting more than albatross?" , "flier" , "It may soar" .)