Dog loses head finding bird of prey (5)
I believe the answer is:
eagle
'bird of prey' is the definition.
(eagle is a kind of bird of prey)
'dog loses head' is the wordplay.
'dog' becomes 'beagle' (beagle is a kind of dog).
'loses head' means to remove the first letter.
'beagle' with its first letter taken away is 'EAGLE'.
'finding' is the link.
(Other definitions for eagle that I've seen before include "A birdie (or better!)" , "good score" , "It normally takes two or three shots to shoot this" , "Bald, golden, bird" , "Fine achievement on course" .)