Ben Zimmer, language columnist for the Wall Street Journal, messaged me the other day:
Are you watching “Succession”? And if so, are you noticing occasional Britishisms sneaking through from the British writers on the show? Tom says “could do” (periphrastic “do”!) talking to Shiv in “Living+,” and Shiv says “Sorry to break up the brains trust” (instead of “brain trust”) in “Tailgate Party.” Of course, Matthew MacFadyen is British and Sarah Snook is Australian, so it’s possible the actors themselves tweaked the lines. Someone also pointed out that “sex pest” was used in a Season 2 episode (by Kendall, I think).
I am perhaps the only person I know who is not watching Succession, so all this was new to me. I had never actually heard of “sex pest,” but just a few days later, someone wrote to the American Dialect Society listserv about a headline on the Jezebel website: “Lauren Boebert Filed for Divorce, and Her Sex Pest Husband Didn’t Take It Well.” None other than Ben Zimmer replied: “‘Sex pest’ is a popular in British tabloid headlines for, e.g., allegations against Prince Andrew. ‘Sex pest’ is actually a useful term, since it implies something a bit less extreme than, say, ‘sexual predator.'”
The OED ‘s definition: “a sex offender; a person who sexually harasses another.” The first citation is what appears to be a headline from The Times in 1985: “Sex pest’s one-way ticket back. A convicted sex offender, sent by a Californian judge..to Florida,..is to be returned to where he came from.”
The phrase has appeared in the New York Times eight times since 1991. They have mostly been in British contexts, including a reference to a report on predatory behavior of Jimmy Savile which said “it appeared to be an ‘open secret’ that Mr. Savile was a ‘sex pest.'” However, that 1991 example was from a humorous essay by American writer Elinor Lipman about the guy at work who “sniffs a woman’s hair at the copy machine and asks what kind of shampoo she uses.” The title was, “Are You the Office Sex Pest?”
In 2020, reviewing Curtis Sittenfield’s novel Rodham, book critic Dwight Garner, a NOOBs icon, wrote, “The portrait of Bill Clinton as sex pest in this novel is dark, and grows darker.” And in 2021, the Times reported on an SNL skit in which a talk-show host introduced Rep. Matt Goetz (played by Pete Davidson) this way: “As we’d say in the early 2000s a hot mess and as we’d say today, a full-on sex pest.”
notoneoffbritishisms.com 
‘Brain’ Trust?
Not sure why it lost its plurality over the pond, but the origins in Britain go back to the 1950s.
“The Brains Trust” was a weekly BBC Home Service radio programme that dealt with various issues that required a panel of professors and the like to elucidate.
It was quite notorious in its own sphere for dealing with obscure and esoteric subjects.
I think we’d call it a’ think-tank’ nowadays.
In normal conversation, it gained some humorous irony when it referred to some-one showing unexpected or obvious knowledge.
However, as a long-gone radio discussion programme – over 50 years ago – the term is not much remembered, (or in usage), here with people younger than their 60s……
But, all very interesting……. I’ll catch up with “Succession” later
Actually, it appears the the brains trust was originally a group of academic advisors to Roosevelt in his 1932 election campaign. It was originally “brains” but the plural was dropped at some point. Presumably after it crossed the Atlantic.
havent owned tv for >2 decades. dont miss it. Writers poorly paid so those without imagination can lounge in fron t of a screen instead of maybe having a life or reading a good book.
“Sex pest” is tabloid-speak — and especially tabloid-headline-speak — for a sex offender. It’s used mainly because it’s short and punchy, suitable for screamer headlines. But it’s a serious allegation used to describe someone doing very serious and highly illegal things.
Your examples sound like it’s being misinterpreted in the US, with “pest” being taken to mean “annoyance”.
It’s reminiscent of years ago, when Americans discovered the verb “chat up” and very badly misinterpreted it to mean something like “make nice”. (Honestly, a salesman shouldn’t be chatting up customers.)
See also Lynne Murphy’s amusement (and disgust) at an American discovering that snog is UK English for kiss and saying he was going to snog his kids.
https://separatedbyacommonlanguage.blogspot.com/2010/04/snogging.html
Hard to say. Savile was clearly a real sex offender, and the fictional portrayal of Clinton and comedic description of Gaetz are based on real accusations, even if they never came to full proof.