Could give the jaywalker a bit of a scare (3)

I believe the answer is:

car

I'm a little stuck... Click here to teach me more about this clue!

'could give the jaywalker a bit' is the definition.
I can't judge whether this defines the answer.

'of a scare' is the wordplay.
'of' indicates the answer is hidden within the clue.
'CAR' is hidden within 'scare'.

Can you help me to learn more?

(Other definitions for car that I've seen before include "Wheels" , "Hatchback, say?" , "Road vehicle; rail coach" , "estate, perhaps" , "Auto" .)

I've seen this clue in the Evening Standard.

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