Quiet safety instruction in car (4,2)

I believe the answer is:

belt up

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'quiet' is the definition.
(both can be used to tell someone to stop talking)

I don't understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for belt up that I've seen before include "Rude instruction to be quiet, or fasten car strap" , "To secure safety strap" , "Stop talking or secure car safety device" , "Be quiet, or secure yourself in car seat" , "prepare to drive!" .)

I've seen this clue in The Guardian.

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