Proprietor of Venice bar sounded rough — in a state! (7)

I believe the answer is:

arizona

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'state' is the definition.
(Arizona is a US state)

I don't understand the rest of the clue.

(Other definitions for arizona that I've seen before include "Site of Grand Canyon" , "State of southwest USA" , "American state with Grand Canyon" , "US state, home to the Grand Canyon" , "US state, capital Phoenix" .)

I've seen this clue in The Times.

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