Pushes out old duster violently (8)

I believe the answer is:

extrudes

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'pushes out' is the definition.
Although both the answer and definition are verbs in their -s form, I can't see how they can define each other.

'old duster violently' is the wordplay.
'old' becomes 'ex' (prefix meaning former or onetime).
'violently' indicates anagramming the letters.
'duster' is an anagram of 'trudes'.
'ex'+'trudes'='EXTRUDES'

Can you help me to learn more?

I've seen this clue in The Hindu.

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