Her mate is spectacularly cocky! (6)
I believe the answer is:
peahen
If this is the answer, I'm afraid I cannot explain it.
Can you help me to learn more?
(Other definitions for peahen that I've seen before include "Mrs Peacock" , "Bird with a showy partner" , "Drab bird" , "Bird, gorgeous-tailed mate" , "Female bird (with a proud partner?)" .)