Momentarily, you may have a hand in it (6)

I believe the answer is:

sleeve

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'hand in it' is the definition.
I know that 'hand' relates to this answer.

I can't explain the rest of the clue.

(Other definitions for sleeve that I've seen before include "Record-holder" , "Tube" , "Part of a shirt - old record holder" , "It covers the arm" , "Some wear their hearts on it" .)

I've seen this clue in the Evening Standard.

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