The part between one's teeth? (3)

I believe the answer is:

bit

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'the part' is the definition.
(both mean a piece of something)

I don't understand the remainder of the clue.

(Other definitions for bit that I've seen before include "scrap" , "Sank teeth in" , "Small fragment" , "Binary digit; small piece" , "Small quantity or piece of metal for a horse" .)

I've seen this clue in the Evening Standard.

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