From Longman Dictionary of Contemporary Englishbuckle up phrasal verbFASTEN/DO UPto fasten your seat belt in a car, aircraft etc → buckle→ See Verb table
Examples from the Corpus
buckle up• Nancy got behind the wheel and buckled up.• The new law will require passengers in the rear seats of automobiles to buckle their seatbelts.• Eighty percent of motorists now buckle up, studies show.