Lena Headey's 'Game of Thrones' Success Made Her Wonder 'What Do I Do' After the Show Ended (Exclusive)

Unless you live Beyond the Wall, you've probably heard of Game of Thrones.

The fantasy show amassed 160 Emmy nominations and became HBO's most-watched series ever. When the series wrapped in May 2019 after eight seasons, 19.3 million people tuned in.

"Thrones was such a surprise," star Lena Headey, who played Cersei Lannister, tells PEOPLE in this week's issue. "But there was no part of me that went, 'Oh, it's done now. Life's going to be easy.' It opened doors, it made certain things easier. It also made things feel harder because you think, 'What do I do?'"

Headey, 49, has done plenty in the years since Thrones ended. She currently stars in another HBO series, White House Plumbers, about the Watergate scandal.

"I didn't know anything about it — big fat zero," admits Headey, who grew up in the U.K.

Playing Dorothy Hunt, the wife of Watergate ringleader and former CIA operative E. Howard Hunt (Woody Harrelson), in the limited series about the '70s political controversy didn't help much.

"I still don't, if you were to quiz me," Headey says of whether she learned anything while making the show. "What I do know is that to get to create this duo with Woody, this sort of portrait of a s---y marriage, was fun."

In addition to Plumbers, Headey will star in the upcoming Netflix western The Abandons, lend her voice to sci-fi animation series New-Gen and direct her first feature film The Trap, based on her short film of the same name.

"I loved every second of it," the Bermuda-born actress says of directing. "I hope I get to do more of it because it's my very happy place."

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Headey has also been enjoying the newlywed phase with her husband, Ozark actor Marc Menchaca, who she quietly married in October.

The five-time Emmy nominee filed for divorce in 2012 and called off another engagement years later, so she never expected to get married again. Headey says she changed her mind because she "met someone who's pretty f---ing great" in Menchaca, 47.

Heady co-parents son Wiley, 13, and daughter Teddy, 7, with her exes, which she calls "an endless journey of learning."

"Co-parenting is all for your children," she explains. "You just have to keep moving forward. It's remembering you want your kids to be proud of your decisions and to understand them. But thankfully, my kids are pretty rad and I love hanging out with them."

Headey says she and her children "don't really talk about" her career, but they've caught on a bit.

"If someone says, 'Oh, you're in Game of Thrones', my youngest now says things like, 'What is Game of Thrones?'" Headey says. "In fact, the other day she went, 'My mommy is in...' And I was like, 'You don't tell people!'"

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Despite the show's controversial ending, Headey says fans have affection for Cersei.

"I just get love," she says. "It's weird when you're on holiday with your kids and you're in the midst of a sandcastle and someone's like, 'Hey!' And you're like, 'Have you seen me?' Those moments still happen, which are bizarre, but people are generally lovely."

After years of wearing regal gowns and armor, Headey hopes to play a more laidback character. "If someone was like, 'You get to wear a big sack and order GrubHub,' I'd be like, 'Sign me up!'" Headey says.

She also has a plan B if for some reason her Hollywood reign ends.

"I'm investigating beekeeping," the mother of two says. "I never went to college, so I cannot actually do anything. My fantasy is keeping bees and making skateboards."

For more on Lena Headey, pick up the latest issue of PEOPLE, on newsstands Friday, or subscribe here.

White House Plumbers airs Mondays at 9 p.m. ET on HBO.