Flier, quickest, relative displays (7)
I believe the answer is:
kestrel
'flier' is the definition.
(kestrel is a kind of birdanimal)
'quickest relative displays' is the wordplay.
'displays' indicates the answer is hidden within the clue.
'KESTREL' is hidden in the letters of 'quickest relative'.
(Other definitions for kestrel that I've seen before include "High-flyer" , "Small type of falcon" , "Les, trek around the bird" , "Falcon that hovers" , "High flier" .)