Chief bird showing off (8)
I believe the answer is:
swanking
'showing off' is the definition.
('swank' can be a synonym of 'show off')
'chief bird' is the wordplay.
I cannot really see how this works, but
'chief' could be 'king' and 'king' is found in the answer.
'bird' could be 'swan' (swan is a kind of bird) and 'swan' is found in the answer.
No letters remain.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for swanking that I've seen before include "Posturing" , "swaggering" , "Pretentious" .)