[keep] a lid on {sth}

to control a situation and stop it from getting worse

The idiomatic phrase "keep a lid on something" has its origins in the United States in the late 19th/early 20th century, deriving from the literal notion of securely fastening a tight-fitting lid onto a container to prevent its contents from spilling out, which then developed figuratively into referring to keeping information contained or suppressed, as evidenced by some early newspaper citations from the late 1800s discussing keeping secrets or scandals tightly guarded. It is frequently used in political, legal, and workplace settings to describe efforts to prevent damaging leaks, skeletons in the closet from being aired out, or potential scandals from emerging.

The fire department is working hard to keep a lid on the out-of-control bushfire before it spreads further.
Hoping to prevent full-scale panic, the CDC will have to keep a tight lid on early reports of the potential outbreak.
By clamping down on misinformation, the government had just barely kept a lid on public hysteria before a vaccine was found.
In the aftermath of the disaster, response teams will have successfully kept a lid on looting and lawlessness until relief arrives.

to not let something become revealed to others

The origin of the idiom "keep a lid on something" stems from the literal usage of lids on containers in the late 19th/early 20th century, as it was common practice to use tight-fitting lids to prevent contents from being spilled or seen. This simple act of securing a lid came to represent concealing what was inside in a metaphorical sense, and one of the earliest figurative usages referred to keeping secrets "under wraps" with a "tight lid," which then developed into newspaper uses by the 1900s employing the phrase such as "keeping a lid on the scandal" to denote suppressing details and maintaining secrecy about a covert matter. It is commonly invoked legally to suppress unflattering evidence or privately settled allegations.

The prime minister is desperately trying to keep a lid on revelations from his former mistress's tell-all book.
No matter their efforts, the leaks kept coming and the organization never fully managed to keep a lid on the payment scandal.
Hoping to avoid public humiliation, several ministers will have to keep an extremely tight lid on private indiscretions after mandatory disclosure laws pass.
Despite years of secrecy, hackers have finally managed to pry open the lid on the company's anti-competitive business practices.
Looking back, historians will remark how remarkably the administration had kept a lid on early warnings about the impending crisis.