Wiktionary
vb. (context idiomatic English) To keep a secret; to refrain from speaking indiscreetly or carelessly; ''broadly'', to refrain from speaking altogether.
WordNet
v. refrain from divulging sensitive information; keep quiet about confidential information; "Don't tell him any secrets--he cannot keep his mouth shut!" [syn: keep quiet, shut one's mouth] [ant: spill the beans]
Usage examples of "keep one's mouth shut".
But in the tiny peacetime Army, one learned to keep one's mouth shut, particularly as the Depression roared around the gates of the camps, and the advantages of a civilian career looked very bleak.
Better to keep one's mouth shut than to lose a commission, he thought sourly—.
An ancient scrap of wisdom drifted through my memory, something to the effect that when it comes to learning, it's best to keep one's mouth shut and ears open.
He knew how hard it was to keep one's mouth shut about such things.