Carrie Mathison of “Homeland” had better watch out — the fictional arm of the CIA has a new maverick agent on the scene, and she doesn’t do “cry faces.”

“Oh, no!” laughs Yvonne Strahovski. The “24: Live Another Day” actress has never heard of Claire Danes’ famous emotive sobbing. Nor has she ever seen Showtime’s “Homeland,” the series to which her own adrenaline-pumping, terrorist-chasing franchise is often compared.

Strahovski, 31, says she plays her super-agent character, Kate Morgan, with a purposeful coldness and detachment. Morgan has been unwittingly married to a traitor, which she and the audience discover as the show opens. Strahovski delivers a star-making performance on the highly anticipated “24” reboot, which premieres May 5 on Fox and picks up four years after the original series ended its nine-year run in 2010 — with Jack Bauer (Kiefer Sutherland) living as a fugitive in London.

“You meet Kate at a point in her life when she’s feeling dejected and doesn’t have a lot to hold onto,” Strahovski says. “When Jack Bauer comes into the picture, and she has an opportunity to make things right and maybe prove herself, she jumps at it, and then turns into someone who’s hunting him in a way. It’s dark.”

Beyond that, Strahovski can’t reveal much more about the closely guarded plot.

The stunning Australian is in New York for a short break from shooting the show on location in London. She’s wearing fitted jeans, a scoop-neck top and strings of dainty Jennifer Meyer necklaces, but when the sun goes down, she slips on a Quiksilver hoodie — a nod to her newfound passion for surfing.

“I really enjoy playing dress-up, doing photo shoots, and I wish I could wear stuff like that by choice, but I will never be that person,” says Strahovski, who claims she’d never heard of Dolce & Gabbana until her first spin on the red carpet several years ago. “I’m such a boots-jeans-tops-blazer girl. If I can’t do high kicks or dance in it, then I won’t wear it.”

Strahovski moved to LA from Sydney — where she was a stage-trained actress and owned a theater company — “just for the hell of it” in 2006, and never used the return ticket home.

“I’ve just discovered Malibu. I had been in Laurel Canyon but sold my house and decided to downsize, pull back a little bit,” she says.

Her parents — Polish immigrants who moved to Australia in the 1980s “with their suitcases and 20 dollars” — followed their only child to California for support. They hated LA and moved back after only two years, but they didn’t need to worry: Small parts immediately poured in for the statuesque blond beauty, followed quickly by meatier recurring roles on Showtime’s “Dexter” (as sultry killer Hannah McKay) and NBC’s “Chuck” (as Sarah Walker, also a CIA agent).

In 2012, Strahovski spent four months in New York in what critics called her “striking Broadway debut” as Lorna in Clifford Odets’ “Golden Boy.” The role, in which she played opposite “Monk” star Tony Shalhoub, earned Strahovski a Theatre World Award.

“Yvonne possesses a rare combination of inner grace, dark mystery and unbridled devilish fun that seems to radiate straight through her arresting beauty,” Shalhoub says. “She is a courageous, deeply sensitive actress.”

To clear her head from her whirlwind career, Strahovski relishes the peace of outdoorsy athleticism, like hiking or rock climbing. (And a little bit of reality TV — she admits she’s a fan of Bravo’s “Vanderpump Rules.”) Surfing has proved to be a particularly unlikely source of calm — Strahovski is terrified of deep water.

“I’m scared of not knowing what’s underneath me, but I was tempted to stand on a surfboard,” she says. “The minute I did it, something happened and I was hooked. I’ve never been good at meditation, but surfing is the closest I’ve ever come to that inner something.”

It’s an added bonus that her boyfriend surfs, which is about all Strahovski is willing to say about him other than that he’s not “Hollywood.” “I like to stay separated from the acting world,” she says of her personal life.

Strahovski will say she’s become buddies with her “24” co-star Gbenga Akinnagbe, who plays CIA field operative Erik Ritter, another new character. “He’s a great guy, like a kid on set,” she says.

As for the star of “24,” Sutherland, she says he “knows the show inside and out. He lives and breathes his character. Between him and Jon Cassar, the in-house director and producer, they really know it very well.”

Cassar says of Strahovski: “Yvonne has been a great addition to the new ‘24.’ Not only is she very comfortable with the physical demands of her character but she moves through those scenes with a gravitas that makes you believe she’s been a CIA agent all her life. And if that isn’t enough, she does it all with a great attitude under very difficult shooting circumstances.”

Strahovski acknowledges shooting is “taxing on your body,” but she carves out time to take care of herself.

“I try and be as natural as I can. Less is more,” she says. “I had an addiction to sugar growing up — major, major, major. I calculated once that I ate about 400 liters of Nutella in a 10-year period. And I had to stop,” she says. “I had terrible skin because of it and I refused to believe sugar was my issue, because so many other people don’t have that problem.”

Banning sugar is as strident as Strahovski gets with her health and diet. For fitness, she relies not on the gym — “I hate putting aside time to work out” — but on what she calls “manual living.” This means using a whisk instead of an electric mixer, biking to the grocery store or taking the stairs instead of the elevator.

“Often in the shower if I’m shaving my legs, instead of resting my foot on something, I’ll stand on one leg and balance,” she says, calling it “accidental yoga.”

Even as she steps further into the spotlight, Strahovski maintains she will stay true to her natural beauty. With a smile, she says, “Crow’s feet are nice.”