Her cocky mate's a real show-off! (6)

I believe the answer is:

peahen

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'show-off' is the definition.
Although both the answer and definition are singular nouns, I cannot understand 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 "Female of a proud-tailed cock" , "Mrs Peacock" , "Female bird (with a proud partner?)" , "Drab bird" , "Bird, gorgeous-tailed mate" .)

I've seen this clue in the Evening Standard.

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