Chauvinists gathered around quiet people with lots of power (3,5)

I believe the answer is:

big shots

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'chauvinists gathered around quiet' is the definition.
I can't tell whether this defines the answer.

'people with lots of power' is the wordplay.
'people' becomes 'shots' (shot is a kind of person).
'with' is a charade indicator (letters next to each other).
'lots of power' becomes 'big' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'shots' after 'big' is 'BIG SHOTS'.

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I've seen this clue in the Sydney Morning Herald.

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