Wiktionary
keep a lid on
vb. (context idiomatic imperative English) To keep something secret.
Usage examples of "keep a lid on".
You're the biggest secret I've ever had occasion to keep a lid on, and already too many people know all about you.
Apparently Robin had managed to keep a lid on knowledge of the rape.
They'd want to keep a lid on their pseudogenics research, on their dealings with Clare, on their Research Center.