A tiny dog, misbehaving, playing up (8)

I believe the answer is:

toadying

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'playing up' is the definition.
Although both the answer and definition are present participle verbs, I don't see how one could define the other.

'a tiny dog misbehaving' is the wordplay.
'misbehaving' indicates anagramming the letters.
'a'+'tiny'+'dog'='atinydog'
'atinydog' anagrammed gives 'TOADYING'.

Can you help me to learn more?

(Another definition for toadying that I've seen is " Obsequious".)

I've seen this clue in The Telegraph.

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