keep (something) on the down low
To keep something in a state of secrecy or minimal public knowledge; to not share something with anyone else. Keep this on the down-low, but Janet is planning to break up with Kevin next week.
keep it on the ˈdown-low
(American English, slang) keep something secret; not tell other people about something: Her parents wouldn’t approve of our relationship so we keep it on the down-low.