keep one's mouth shut
Be quiet; don't reveal confidential information. For example, The teachers told us to keep our mouths shut during the entire presentation, or You can't tell Carol anything; she's incapable of keeping her mouth shut. Also see hold one's tongue.
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.