Carnivore hunting yak and elk notices antelope first of all (6)
I believe the answer is:
hyaena
'carnivore' is the definition.
(hyaena is a kind of carnivore)
'hunting yak and elk notices antelope first of all' is the wordplay.
'first of all' indicates taking the first letters.
The first letters of 'hunting yak and elk notices antelope' is 'HYAENA'.
(Other definitions for hyaena that I've seen before include "creature after one's body" , "African carnivore" .)