Theatre veteran J. Smith-Cameron nails the 50 shades of Gerri in HBO's Succession

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 this week returned 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 favourite, 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 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. (A 35-minute YouTube compilation of Gerri and Roman's greatest moments has racked up more than 200,000 views and hundreds of comments).

"The majority of my career has been in theatre. 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, 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. In the season ahead, which resumes in the immediate wake of this very public betrayal, 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. "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."

Executive producer Frank Rich says Smith-Cameron has a range expansive enough to capture all 50 shades of Gerri.

"J. can do a kind of playful, witty, comic turn, but you also believe that she has nerves of steel that have allowed her to be successful in business. She keeps finding new things in the character and the writers keep finding new things and know that she is an instrument that can hit any note."

Growing up in Greenville, South Carolina, Smith-Cameron - then known as Jeanie Smith - played the violin but shied away from acting; it had been her older sister's thing. Then a friend convinced her to try out for the school play, The Diary of Anne Frank. She got the part. She also got contact lenses. "My whole personality changed," she says.

She eventually started going by J. - Jeanie was too girly, she decided - and added Cameron, a family name, when she got her Actors' Equity card.

Throughout most of the '80s and '90s, she worked on the stage, often in comedic roles, such as the fast-talking con artist she played in Douglas Carter Beane's As Bees in Honey Drown. She took occasional roles in film and TV, including a supporting part in the groundbreaking dramedy The Days and Nights of Molly Dodd.

But she resisted the push to fly out to LA for pilot season. "Agents and casting directors thought I was a shoo-in for sitcoms, like the Shelley Long-type parts," she says. "Performing live is very heady and exciting. So I was just always working."

Smith-Cameron began to focus more on TV and film once she started a family and wanted to be at home - not onstage - for bedtime. Luckily for her, this change of heart happened to coincide with "TV becoming more interesting", she says.

For four seasons, she starred as the world-weary mother of a recently freed death row inmate in the contemplative Sundance drama Rectify. The languidly paced series was a critic's darling but never reached the deafening levels of cultural conversation that Succession has inspired.

Don't expect her to play hard-nosed corporate executives in the near future, though. "Sometimes when you have a part that people like so much, it can be kind of crippling, in a way. Because people want you to be that part. "

Three seasons in, though, Gerri remains a bit of a mystery - a career woman whose extracurricular life is mentioned fleetingly and never seen. A cursory backstory can be stitched together using scraps of dialogue: Her husband Baird died, possibly in an incident involving a tortoise; she's godmother to Logan's only daughter, Shiv (Sarah Snook); she has two grown daughters who apparently enjoy flying on the company dime. Beyond that, she's an enigma in Stuart Weitzman boots.

Smith-Cameron has formulated her own ideas about Gerri's past, ones that haven't necessarily gotten Armstrong's stamp of approval but are useful to her understanding of the character. She thinks Gerri's late husband was much older than her and helped her land a job at Waystar Royco through his friend, Logan. She also wonders if Gerri and Logan ever had a thing.

"I imagine there was some kind of connection between Logan and Gerri, maybe something illicit, I don't know," she says. "Or maybe just admiration. And he helped her and that bond is still there, of people who've slept together or flirted or spent all-nighters figuring their way out of something."

Smith-Cameron also initially proposed the idea that Gerri has daughters - inspired, she says, by a number of "really remarkable, outspoken, brainy older women" she'd known whose grown daughters both adored and feared them, and "had to move across the globe in order to really figure out who they were".

The relationship with Roman, baffling though it may be, has illuminated another side of Gerri.

No doubt the audience is happy to keep speculating about what's next for Roman and Gerri - and writing slime-puppy fan fiction in their spare time. But they should probably adjust their expectations; this is Succession after all. "There are fans who would like them to be married with children," she says. "And I don't think it goes that way."