To refrain from talking, to hold one's tongue, to be quiet.
hold one's tongue
To refrain from talking about something.
zip one's lip
To refrain from or to stop talking; to be quiet; shut up.
keep quiet
To refrain from talking about something; to keep a secret.
put a lid on it
To be quiet; to shut up; to stop talking about something or making noi…
shut one's mouth
To stop talking; to be quiet.
shut one's face