Bird makes dog lose head (5)
I believe the answer is:
eagle
'bird' is the definition.
(eagle is a type of bird)
'dog lose head' is the wordplay.
'dog' becomes 'beagle' (beagle is a kind of dog).
'lose head' means to remove the first letter (lose (remove) the head (start) of the word).
'beagle' with its initial letter taken away is 'EAGLE'.
'makes' acts as a link.
(Other definitions for eagle that I've seen before include "Fine achievement on course" , "Aglee (anag.)" , "Raptor" , "A birdie (or better!)" , "somewhat under par" .)