Alexander Skarsgård has been so busy he didn't need a place to live for two years

How busy is Alexander Skarsgård? Busy enough that he recently spent years without a home to call his own. “I’ve just been living on location, jumping from one project to another,” says the True Blood and Big Little Lies actor. “I actually got an apartment in New York a few months ago. That was the first time in two years I had my own bed.”

Skarsgård has already starred in a pair of 2018 Netflix thrillers — Mute and Hold the Dark. Now the Swedish actor is playing an Israeli intelligence officer named Gadi Becker in the AMC miniseries The Little Drummer Girl (currently airing nightly), an adaptation of John le Carré’s espionage novel. Set in the late ’70s, Drummer Girl costars Florence Pugh (Lady Macbeth) as Charlie Ross, an actress who is recruited by Skarsgård’s character to help stop a bombing campaign in Europe. “A young British actress in Greece walks into a quite enigmatic man, who she initially thinks is just a budding holiday romance,” says Skarsgård of the relationship. “He turns out to be something completely different, and she’s roped into a world of international espionage.”

In the miniseries’ first installment, Gadi takes Charlie to the Acropolis in Athens for what she believes is a romantic date. Skarsgård fondly recalls shooting at the historic site. “They closed down the Acropolis from sundown to sunrise for us,” says the actor. “It felt very, very special to be up there watching the sunset over Athens.”

Drummer Girl is helmed by legendary South Korean director Park Chan-wook (Oldboy); Skarsgård is a big fan. “He’s one of the greatest filmmakers of our time,” says the actor. “There are directors that have a visual language that is sometimes at the expense of the characters. They’re focused more on the visual aspect than on the psychology of the story. He is a master at both.”

One thing Skarsgård shares with his character? The actor admits he’s “pretty good” at keeping secrets, and proves it when EW asks whether he will appear in the second season of HBO’s Big Little Lies (set to premiere in 2019). Skarsgård’s character, the abusive Perry Wright, died in the first season, but the actor was spotted on the set of season 2, prompting speculation that Wright might make some kind of from-beyond-the-grave appearance. “Well, my character is definitely dead,” he says. “I can’t say any more.”

The actor is more forthcoming about his role in the comedy Flarsky (out June 7), about an out-of-work journalist (Seth Rogen) whose childhood babysitter (Char­lize Theron) becomes one of the world’s most powerful women. “Charlize Theron’s a friend of mine, and they were also shooting in Montreal, and so she asked if I wanted to come in and play the prime minister [of Canada]. It’s not [Justin] Trudeau, but it’s definitely loosely based on him,” Skarsgård says of his role in the movie, a part he filmed on his days off from the set of The Hummingbird Project, his upcoming drama with Jesse Eisenberg. All this on top of starring alongside Keira Knightley in the post-WWII drama The Aftermath (April 26) and recently being cast in a dramatization of Dan Krauss’ 2013 documentary The Kill Team, which details the deaths of Afghan civilians by American soldiers. See? We told you he was busy. And currently the actor is tackling his biggest project to date, Godzilla vs. Kong (May 22, 2020). So, who’s the towering thesp playing: King Kong or Godzilla? “I can’t reveal which of the behemoths I am!” he says with a laugh. “No, I play a teeny-tiny little human who tries to not get trampled. I fly out to Hawaii in two days to start that.” Sounds like he doesn’t need that apartment after all.

Watch the trailer for The Little Drummer Girl, above.

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• The Little Drummer Girl star Michael Shannon didn’t think he could play a spy