Not charged in public punch-up: that's not for all (4)

I believe the answer is:

free

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'not charged in public' is the definition.
'free' can be an answer for 'public' (thesaurus). I'm not certain of the 'not charged in' bit.

I don't understand the remainder of the clue.

Can you help me to learn more?

(Other definitions for free that I've seen before include "Not busy" , "Release - without charge" , "Complimentary" , "Release; gratis" , "Pro bono" .)

I've seen this clue in The Guardian.

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