'Be quiet'. Also, since the introduction of car seat belts - an injunction to fasten one's belt.
UK slang. This is first cited by Eric Partridge in his 1949 A Dictionary of Slang:
Belt up: Shut up!: R.A.F.: since circa. 1937.
The seat belt usage came in the UK in 1983, when the Ministry of Transport introduced legislation to enforce the wearing of car seat belts. This is from a newspaper headline, 1st January 1983:
"British drivers ordered to belt up - Drivers and front seat passengers must wear seatbelts under a new law which came into force at midnight."