US independent study with arbitrator (7)

I believe the answer is:

mugwump

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'us independent' is the definition.
'mugwump' can be an answer for 'independent' (synonyms). I'm not certain of the 'us' bit.

I don't understand the remainder of the clue.

Can you help me to learn more?

(Other definitions for mugwump that I've seen before include "(In American) boss man" , "Fence-sitter (originally, big chief)" .)

I've seen this clue in The Guardian.

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