For safety’s sake a motorist should be quiet! (4,2)
I believe the answer is:
belt up
I believe this is a double definition.
'for safety's sake a motorist should' is the first definition.
(belt up can mean to wear a seat belt in a car)
'quiet' is the second definition.
(both can be used to tell someone to stop talking)
'be' acts as a link.
(Other definitions for belt up that I've seen before include "Rudely silence" , "Fasten oneself in to a car seat - keep quiet!" , "take safety precaution" , "Strap yourself in - keep quiet!" , "put a sock in it!" .)