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It's the British version of shut up.

Could also mean 'fasten your seatbelt'.
1. She told the students to belt up because they were making so much noise.

2. I told the kids to BELT UP before I started the car.
by Valda Tichenor July 10, 2006
british slang for shut up, a rude way to tell someone to be quiet.
belt up you bloody crony
by dragacrone January 23, 2013