To stop talking
To stay calm
To remain secret or silent
Zipping your lip is one difficult task for a fellow to likes to speak his heart out.
The manager asked all those who disagreed with the new rule about shortening of the lunch breaks to zip their lips.
It is almost impossible to zip your lip when you are in the company of family or friends.
Anyone who wishes to stop talking should just zip their lip.
There is no origin for this idiom
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definition
Common phrase that has a specific meaning.