When she was first approached about playing Siobhan “Shiv” Roy, the only daughter of a ruthless but ailing media tycoon in HBO’s “Succession,” Sarah Snook was apprehensive of the project despite its obvious pedigree.

As a performer on the rise, thanks to a string of award-winning film and television roles in Australia and a well-received turn in the 2015 biopic “Steve Jobs,” Snook was wary of being marginalized in a show that, at first glance, seemed to be about “a bunch of white men in business.”

“Do I want to be a prop in this story that doesn’t focus on me at all?” she recalled recently at a cafe in Williamsburg, Brooklyn, near the apartment where she lives while filming “Succession.” “I read the pilot and went, ‘I want to watch this, but I don’t know if I want to be in it.’”

Snook’s trepidation was understandable, particularly given the gender dynamics of prestige TV circa 2016 when, as she put it, “‘Game of Thrones’ was huge and there was a leaning across the board in TV for more female nudity.” Thankfully, it also turns out to have been misplaced: Shiv has proved to be an essential player in the cynical, male-dominated world of “Succession,” which returned to HBO for its fourth — and, as recently announced, final — season on March 26.

The news that “Succession” would end with Season 4, first reported by the New Yorker last month, caught many fans off guard — and, it seems, some of the cast. Snook said that, despite indications throughout production that the show might be winding down, she was not officially informed until the final table read in January.

“I was very upset,” she said a few weeks after our Brooklyn meet-up, in a follow-up call from Melbourne. “I felt a huge sense of loss, disappointment and sadness. It would have been nice to know at the beginning of the season, but I also understand not being told until the end because there was still a potential that maybe this wasn’t going to be the end.”

“Emotionally, all of us weren’t necessarily ready to be done with the show because we love each other so much,” she added. “But everything has to come to an end, and it’s smart not to let something become a parody of itself.”

Created by British writer Jesse Armstrong, the Emmy-winning saga follows Logan Roy (Brian Cox), a cantankerous self-made billionaire, and the grown children desperate to win his approval and take over Waystar Royco, the family’s vast news and entertainment conglomerate. “Succession” offers viewers a glimpse of life inside a powerful media dynasty — of the Mediterranean superyachts and tricked-out private jets, but also of the corrosive family dysfunction that can accompany extravagant wealth.

The vicious sibling rivalry and thorny parent-child relationships are what makes “Succession” relatable, even to those of us who’ve never set foot in Davos. Like her older brothers Kendall (Jeremy Strong), Roman (Kieran Culkin) and Connor (Alan Ruck), Shiv has profound daddy issues, ones that are magnified by her status as the only woman in the family. (Her mother, played with bone-chilling detachment by Harriet Walter, is a spectral presence in her life.)

As sharp and merciless as her namesake, Shiv rivals her father in terms of sheer cunning. Her Machiavellian exploits include dissuading a former employee from testifying before a Senate committee about the sexual misconduct at Waystar and leaking details about Kendall’s struggles with addiction and mental illness to the press. But Season 4 finds Shiv at a nadir: ousted from the company and estranged from her once devoted husband Tom Wambsgans (Matthew Macfadyen) following an unthinkable betrayal.

Snook, it bears mentioning, could scarcely be less like Shiv: An unfussy and self-deprecating Australian, she exhibits none of her character’s frosty entitlement in person, showing up at a quiet cafe in a gray hoodie and weathered Blundstone boots. When a scheduling mishap sends me to the wrong borough for our meeting, she texts me the correct address and patiently waits in Brooklyn while I take a cab across the river.

Still, Snook has taken lessons from Shiv, particularly the confidence “that she is allowed to be anywhere. She doesn’t believe in a glass ceiling, because she could buy the building.”

Though you might not know it from her nearly seamless American accent on the show, Snook grew up outside Adelaide — the city where Rupert Murdoch, the loose inspiration for Logan Roy, launched his newspaper empire.

The youngest of three sisters, Snook displayed a performative streak early on, winning a high school drama scholarship and — in what might qualify as her first paid acting gig — working as a children’s party entertainer named Fairy Lavender. (She continued the hustle when she moved to Sydney to attend the prestigious National Institute of Dramatic Art, but she had to change her name to Fairy Twinkle Toes; Sydney already had a Fairy Lavender.)

The job gave her an early lesson in winning over a skeptical audience. “You’d get a lot of kids going, ‘I don’t know if I believe in you,’” she said. “That’s kind of what Shiv does when she walks into a room and is like, ‘You have to believe that I’m capable of doing this.’”

After finishing her studies at NIDA, Snook had steady work in Australian theater, film and TV.

Hollywood quickly took notice: She was one of the final candidates to play Lisbeth Salander in “The Girl With the Dragon Tattoo “ (the role ultimately went to Rooney Mara). In 2014, she starred with Ethan Hawke in the heady sci-fi yarn “Predestination,” delivering an audacious performance as an intersex character who lives first as a woman, then a man. Snook’s male persona — who bore an uncanny resemblance to, as she put it, Leonardo DiCaprio’s “less attractive brother” — was so convincing, her own mother didn’t recognize her on set.

“Finding the character was easier for me than being, like, the hot surfer girl,” she said. “To be a man? That’s great.”

In quick succession, she went from “The Dressmaker,” a period piece set in rural Australia, to “Steve Jobs.” Then came “Succession.”

Casting director Francine Maisler, an early champion of Snook’s work, had brought Snook to the attention of Adam McKay, who directed the pilot, and Armstong, who was struck by the blend of intelligence, toughness and humanity she brought to her audition.

“Suddenly, you go from thinking, ‘Oh my God, will there be anyone?’ to ‘Oh my God, I hope she hasn’t gotten any offers,’” Armstrong recalled by phone during a break from editing “Succession.”