“Catch and kill” is the process that a tabloid newspaper buys and then buries a news story. The newspaper pays for the exclusive rights to the story, and then decides not to publish it—preventing any news from getting out.
 
It’s not known when “catch and kill” was first used in journalism. The Wall Street Journal‘s story on November 4, 2016 about presidential candidate Donald Trump, a Playboy model and the National Enquirer newspaper populared the “catch and kill” term.
 
     
The Wall Street Journal
National Enquirer Shielded Donald Trump From Playboy Model’s Affair Allegation
Tabloid owner American Media agreed to pay $150,000 for story from 1998 Playmate of the Year, but hasn’t published her account
By JOE PALAZZOLO,  MICHAEL ROTHFELD and LUKAS I. ALPERT
Nov. 4, 2016 9:29 p.m. ET
1729 COMMENTS
The company that owns the National Enquirer, a backer of Donald Trump, agreed to pay $150,000 to a former Playboy centerfold model for her story of an affair a decade ago with the Republican presidential nominee, but then didn’t publish it, according to documents reviewed by The Wall Street Journal and people familiar with the matter.
 
The tabloid-newspaper publisher reached an agreement in early August with Karen McDougal, the 1998 Playmate of the Year. American Media Inc., which owns the Enquirer, hasn’t published anything about what she has told friends was a consensual romantic relationship she had with Mr. Trump in 2006. At the time, Mr. Trump was married to his current wife, Melania.
 
Quashing stories that way is known in the tabloid world as “catch and kill.”
   
Washington (DC) Post
‘Catch and kill’ at National Enquirer gives media one last black eye before election
By Margaret Sullivan Media Columnist November 5 at 3:59 PM
In the tabloid business, the practice is called “catch and kill.”
 
That phrase was circulating on Saturday after the Wall Street Journal’s solidly reported story that the National Enquirer — no stranger to checkbook journalism — had laid out $150,000 in August to a former Playboy magazine Playmate, who says she had a lengthy adulterous affair with Donald Trump a decade ago.
 
The paper paid for exclusive rights to Karen McDougal’s story but never published it, the Journal reported. Thus: catch and kill, otherwise known as trapping a story to keep it out of the public eye, for one reason or another.
 
Slate
NOV. 5 2016 7:41 PM
National Enquirer Allegedly Paid to Kill Story of Playboy Playmate’s Affair With Trump
By Daniel Politi
(...)
In August, the National Enquirer sealed a $150,000 contract with Karen McDougal, who was the 1998 Playmate of the Year and told friends she had a 10-month consensual relationship with Trump while he was married to Melania. McDougal apparently thought the tabloid would publish a story on the alleged affair but it never happened, apparently pulling what is known as a “catch and kill” in the tabloid business. According to a contract reviewed by the Journal, McDougal was forbidden from going with her story elsewhere.