NEW YORK — At the Carlyle hotel, a pair of Upper East Side doyennes are discussing their country homes between mincing bites of their $30 salads.

A few feet away, J. Smith-Cameron is talking about slime puppies.

"I made up slime puppy," says the actor, in a crisp white blouse and polished blond bob. "I'm proud of slime puppy. It's my contribution to American literature."

In HBO's caustic, Emmy-winning drama "Succession," which returend this fall for its long-delayed third season, Smith-Cameron stars as Gerri Kellman, general counsel to Waystar Royco, the media and entertainment conglomerate run by the rapacious Roy family.

Her character has grown into something of a fan favorite, thanks in part to a sordid entanglement with her much younger colleague, Roman Roy (Kieran Culkin), who is also the youngest son of Waystar's fearsome founder, Logan Roy (Brian Cox).

When a late-night call unexpectedly turned into a kinky phone-sex session last season, Gerri purred degrading insults at Roman. These included "slime puppy," a strangely evocative epithet that has been embraced by the internet's many Gerri-Roman shippers — and one that suddenly came to Smith-Cameron during a round of improv.

"I don't even know what it means," she says with a wry laugh. "But it suits him."

Though she has worked steadily for more than four decades, Smith-Cameron is now best known for playing Gerri, a role that has brought her a level of fame — and type of fandom — rarely achieved by 64-year-old character actors with names reminiscent of tweedy classics professors.

"The majority of my career has been in theater. That just naturally has a smaller audience, and I was quite content with that. I played all these great roles," says Smith-Cameron. The actor, who seems to share Gerri's refined fashion sense — she arrives at the Carlyle in a crisp white blouse, dark trousers and chic librarian glasses — is also just as sharply witty, someone you could easily imagine confiding in over a stiff cocktail.

At lunch, Smith-Cameron jokes about being an empty-nester now that her daughter, 19, is off at college in Scotland. Her husband, playwright and filmmaker Kenneth Lonergan, "is really miserable" about the change, she says. "I was like, 'Kenny, she hasn't been talking to us for years. What's the difference?'"

Everything about "Succession" has been "completely unexpected," she says, "right down to Gerri not really being this character at all to begin with."

Originally written as a man and only meant to appear in a handful of episodes, Gerri has evolved into a pivotal player in "Succession," created by former "Veep" writer Jesse Armstrong.

A fixer, consigliere and billionaire whisperer all in one, she is not only an indispensable ally to Logan but also the closest thing his four adult children have to a maternal figure. Fiercely loyal to the Roys, she also quietly registers her disapproval of their loathsome behavior through the occasional wince, which amounts to an act of moral bravery in the depraved world of "Succession."

Season 2 concluded with a stunning press conference in which Kendall Roy (Jeremy Strong) described his father as "a malignant presence, a bully and liar" who was aware of widespread abuse within Waystar Royco's cruise division. This season, Gerri's role at the company is even more prominent.

"It's happened a little bit with the show that when someone joins us and the storylines open up, there's room for us to expand a role," says Armstrong in an email. "And obviously J. is so talented we know she will be able to go wherever the story leads."

Smith-Cameron suspects that as an outsider who can roll her eyes at the Roys, she provides a release for the audience. And as "a middle-aged woman character who is canny and clever," Gerri is particularly appealing at a moment when the culture is more receptive to stories about older women (see also: Jennifer Coolidge in "The White Lotus," Jean Smart in everything). "She's sexual without being a sexpot, without being glamorous," Smith-Cameron says. "I think people have come around to really wanting that.

"It's so much more interesting than in the '80s. If there was a character over 40 who was a businesswoman or a lawyer, she was a barracuda," she continues. "Gerri is very capable, but she bites her nails. She's not someone who's invulnerable. She's ordering that martini for a reason."

Culkin and Smith-Cameron have a connection that dates back years before "Succession." They'd both starred in projects by Lonergan, including the film "Margaret" and the play "The Starry Messenger," and have a naturally spiky rapport.

"I feel like she's told me on several occasions how much she hates me. And I know that that's her telling me that she loves me," says Culkin, who tells a story about going up to Smith-Cameron on set one morning and greeting her: "Hi, Mommy Girlfriend." She started calling him "Baby Man" in response.

Culkin says he would often go home and tell his wife he hoped the writers would go there with their characters "because I've just been really flirty with her all season."

Armstrong is reluctant to speculate about what, exactly, Roman sees in Gerri, and vice versa, but he concedes that "it's an interesting knot to examine with the audience."