Her mate makes a cocky display (6)
I believe the answer is:
peahen
'display' is the definition.
Although both the answer and definition are singular nouns, I cannot see how one could define the other.
I don't understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for peahen that I've seen before include "Mrs Peacock" , "Female of a proud-tailed cock" , "Female peacock" , "Bird, gorgeous-tailed mate" , "Bird with a showy partner" .)