Hesitate when not quite sober (5)

I believe the answer is:

demur

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'hesitate' is the definition.
(I've seen this in another clue)

I can't explain the rest of the clue.

(Other definitions for demur that I've seen before include "Hesitate from uncertainty or object" , "Waver" , "'Object, show reluctance (5)'" , "Raise mild objection" , "Hesitation" .)

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

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