Meaning
To keep quiet / To zip it
Example
É melhor você ficar de bico calado sobre o que viu ontem à noite.
You better keep quiet about what you saw last night.
Origin
The image is transparent: bico literally means "beak," used colloquially for the mouth, so ficar de bico calado is to keep one's beak shut — to stay silent and let nothing slip.
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More idioms
Acertar na moscaTo guess correctly / To hit the nail on the headAmigo da onçaA fake/false friendAndar na linhaTo toe the line / To behave properlyArmar um barracoTo cause a public sceneRodar a baianaTo cause a public scene / To go ballisticArrumar sarna pra se coçarTo ask for troubleArrastar as asasTo hit on someone / To flirtAbrir o jogoTo come clean / To open upArregaçar as mangasTo roll up one's sleeves / To get to workAgarrar com unhas e dentesTo hold on for dear life / To seize an opportunity