It's certainly not a new thing at American Media Inc. (AMI) / National Enquirer. There's a 2005 LA Times story that they (AMI) did the same thing in 2003 with a story on Arnold Schwarzenegger, who at the time was developing a close business relation with AMI.
Days after Arnold Schwarzenegger jumped into the race for governor and girded for questions about his past, a tabloid publisher wooing him for a business deal promised to pay a woman $20,000 to sign a confidentiality agreement about an alleged affair with the candidate.
American Media Inc., which publishes the National Enquirer, signed a friend of the woman to a similar contract about the alleged relationship for $1,000.
On Aug. 14, 2003, as candidate Schwarzenegger was negotiating a consulting deal with American Media, the company signed its contract with Mora, who said she received $1,000 cash in return. Goyette declined to say whether she received the $20,000 promised in her contract. [...]
But American Media was effectively protecting Schwarzenegger's political interests, said a person who worked at the company when the contracts were signed. At the same time, American Media was crafting a deal to make Schwarzenegger executive editor of Flex and Muscle & Fitness magazines, helping to lure readers and advertisers.
If American Media was buying exclusive rights to the women's stories, said the person, who has a confidentiality agreement with the company and spoke on condition of anonymity, "why didn't the stories run? That's the obvious question."
"AMI systematically bought the silence" of the women, said the person. Schwarzenegger "was a de facto employee and he was important to their bottom line."
Schwarzenegger biographer Laurence Leamer wrote in his book, "Fantastic: The Life of Arnold Schwarzenegger," that Schwarzenegger understood the tabloids would not skewer him if he was entering a business relationship with the company -- although Schwarzenegger told Leamer he did not specifically seek such assurances.
Indeed, during the recall campaign, American Media put out a 120-page magazine celebrating Schwarzenegger as an embodiment of the "American dream."
The Enquirer did run a story repeating allegations in the British media that Schwarzenegger had an extramarital affair. The story was published first on its website before the election, and then in the newspaper three weeks after his election victory. But it was not prominently displayed, running on Page 24.
The phrase "catch and kill" is not used in that 2005 article, so the term-phrase may be newer than the practice. (N.B. there's a much more widely used term "kill fee" which refers to a freelancer getting only a small payment for a non-published story.)
And in 2009, the Guardian reported [in a headline] that
US golfer gave exclusive interview to sister paper of National Enquirer in return for tabloid's silence
This story doesn't clearly involve outright buying anything because it's not made clear where photos originated from (National Enquirer's own photographers or bought from freelance paparazzis). Although Woods denied any blackmail, there was again a source inside National Enquirer claiming otherwise:
Representatives acting on behalf of Tiger Woods brokered a deal two years ago to bury a tabloid story of an extramarital affair, the Wall Street Journal reported yesterday. It said representatives for the golfer acted after the National Enquirer threatened to publish pictures of Woods taken in a parked car with Mindy Lawton, a Florida waitress.
The alleged deal, which the Wall Street Journal claims was made in August 2007, saw Woods give an exclusive cover interview and photo spread to a sister magazine of the Enquirer, Men's Fitness.
It is the second such claim to be made after the publication of a similar story in the New York Post earlier this month.
American Media, owner of the Enquirer and Men's Fitness, said descriptions of such a deal were "inaccurate, false" and "misinformed". It claimed the interview, headlined Tiger!, and in which a beaming Woods appeared on the cover, was a result of the golfer's previous link with the interviewer, Roy Johnson.
But Neal Boulton, former editor in chief of Men's Fitness at the time of the alleged deal, fuelled further speculation after claiming that he left his post because of the incident. "[American Media CEO] David Pecker knew about Tiger Woods' infidelity a long time ago … He traded silence for a Men's Fitness cover," Boulton told the New York Post.
Also, An AP story has a bit more background on NE's interesting approach to journalism:
Though sometimes dismissed by mainstream publications, the Enquirer’s history of breaking legitimate scoops about politicians’ personal lives — including its months-long Pulitzer Prize-contending coverage of presidential candidate Edwards’ affair — is a point of pride in its newsroom.
During the 2016 presidential campaign, the Enquirer published a string of allegations against Trump’s rivals, such as stories claiming Democratic rival Hillary Clinton was a bisexual “secret sex freak” and was kept alive only by a “narcotics cocktail.”
Stories attacking Trump rivals or promoting Trump’s campaign often bypassed the paper’s normal fact-checking process, according to two people familiar with campaign-era copy.
The tabloid made its first-ever endorsement by officially backing Trump for the White House. With just over a week before Election Day, Howard, the top editor, appeared on Alex Jones’ InfoWars program by phone, telling listeners that the choice at the ballot box was between “the Clinton crime family” or someone who will “break down the borders of the establishment.” Howard said the paper’s coverage was bipartisan, citing negative stories it published about Ben Carson during the Republican presidential primaries.
Simply offering hush money for silence, legalized as an NDA (non-disclosure agreement) is a much wider practice. The usual way this is done is through lawyers. "Catch and kill" is basically the same thing done by a media organization, possibly with the addition of a duplicity element, if the source does not suspect the story is being bought just to be buried. As people are often enough represented by lawyers in such dealings with the tabloid media, it comes with little suprrise that the duplicity element apparently extended to the lawyer representing one of the sources in Trump story, but the duplicity was not maintained all the way through, either by the laywer or by AMI (in this case):
Ms. McDougal maintains that she was duped by a “catch-and-kill” scheme in which Davidson, ostensibly her lawyer, colluded with Cohen and American Media Inc., the parent company of the National Enquirer. In such a scheme, a media company buys the exclusive rights to a story but then buries it, rather than publish it. AMI’s chief executive, David J. Pecker, is reputed to use the catch-and-kill tactic on behalf of allies, and is said to be a friend of Trump’s.
McDougal decided to tell her story in May 2016 — when Trump was plowing through the GOP primaries. Through a mutual friend, she found Davidson, who told her that a deal with AMI could result in a “seven-figure publishing contract” with an initial $500,000 payment in an escrow account. But after an AMI official interviewed her extensively, the company initially declined to buy the story and Davidson confessed that there was no escrow money. AMI explains that it chose not to publish the story because it could not be verified, but concedes discussing McDougal’s allegations with Cohen “as part of its reporting process.”
Weeks later, though, when McDougal was in negotiations with ABC News, Davidson informed her that AMI had a new proposal: AMI would buy her story but not publish it owing to Pecker’s relationship with Trump. The company would pay $150,000 (a sizable chunk of which went to Davidson). The deal was especially attractive to the model-turned-fitness-instructor because she was additionally promised that AMI would run her fitness columns and feature her on at least two publication covers. As the details were being ironed out on August 5, 2016, Davidson was in email and phone contact with Cohen, assuring him the deal was done. McDougal signed it the next day. The story was buried but the fitness columns and covers never materialized.
So at least this "catch and kill" affair devolved simply into a somewhat elaborate hush money/benefits in return for silence; of course, then there was a non-fulfillment (even potential fraud) of the contract by AMI. But my point with this last snippet is that the line between "catch and kill" and just hush money (promises) can sometimes be blurry.