keep quiet
stay quiet
stay silent

For the time being, Peters was staying quiet about the development.

We stayed quiet, but inside I was getting more and more tense.

They've done an excellent job of staying quiet and leaving no trail.

I decided, that he is simply thinking out loud, and stayed quiet.

Who else stood to gain so much if she could be frightened into staying quiet?

His focus now is on "staying quiet," as he puts it - being still.

He went down behind the desk and stayed quiet.

The red house baked under the sun and stayed quiet.

The decent people staying quiet because they don't want trouble.

All this time, he had been standing to the side, looking mad, but staying quiet.