zip your lip informal
none of your lip informal

Zip your lips, is the universal message, and get with the program.

To zip your lip is to shut up.

"Dana, zip your lip and siddown!

"You are traveling to a different dimension, a dimension of " "Bushmaster," Schmidt snapped irritably, "zip your lip."

So, parents, zip your lips when your little darlings approach the crisp white linen bedspreads, pillows and slipcovers with their inevitably sticky fingers and apple cores.

Parkyakarkus - "Zip Your Lip" (Written by Lew Pollack and Tony Stern)

When you enter the low-wage workplace-and many of the medium-wage workplaces as well-you check your civil liberties at the door, leave America and all it supposedly stands for behind, and learn to zip your lips for the duration of the shift.