Peter, possibly a pet (6)

I believe the answer is:

rabbit

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'pet' is the definition.
(a rabbit might be kept as a pet)

I cannot understand how the rest of the clue works.

(Other definitions for rabbit that I've seen before include "Inferior player" , "Poor performer" , "Furry, burrowing animal" , "Chatter; poor games-player" , "Small mammal (not good at sports)" .)

I've seen this clue in the Evening Standard.

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