keep quiet
shut one's mouth
keep one's mouth shut

He started to say something, and then shut his mouth.

I shut my mouth for the next four or five hours.

But I shut my big mouth and let her change the subject.

Why don't I ever learn to just shut my mouth?

She shut her mouth, and thought the rest for them only.

I started to ask him where he was going and then shut my mouth.

If someone had asked me to keep my mouth shut on the subject I might have.

Thank God she'd kept her mouth shut about who the true father was.

You keep your mouth shut and do what you're told!

I think he just kept his mouth shut and died like the rest of them.