Not a dog act, possibly (3)

I believe the answer is:

cat

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'not a dog' is the definition.
I can't tell whether this definition defines the answer.

'act possibly' is the wordplay.
'possibly' is an anagram indicator.
'act' is an anagram of 'CAT'.

Can you help me to learn more?

(Other definitions for cat that I've seen before include "Domestic animal" , "Feline - whip" , "A tom" , "Lash < jazz fan" , "Malicious gossip" .)

I've seen this clue in the Evening Standard.

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