The part a rabbit can’t be without (3)

I believe the answer is:

bit

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'be without' is the definition.
I can't judge whether this defines the answer.

'the part a rabbit can't' is the wordplay.
'the part' indicates the answer is hidden within the clue.
'BIT' is hidden within 'rabbit cant'.

Can you help me to learn more?

(Other definitions for bit that I've seen before include "Mouthpiece of brindle or tip of drilling tool" , "Small fragment" , "Data measurement unit" , "Unit of information" , "Sank teeth in" .)

I've seen this clue in the Evening Standard.

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