Ripley, the indomitable action hero played by Sigourney Weaver in the Alien series, may have hung up her flamethrower for good, but the franchise’s latest prequel, Alien: Covenant, features a convincing replacement in the form of tough cookie Daniels, played by Katherine Waterston. The 37-year-old actor got her breakthrough role as the enigmatic Shasta Fay in Paul Thomas Anderson’s fuzzy comic thriller Inherent Vice and was last seen sporting a cloche hat and brandishing a wand as Tina in Fantastic Beasts and Where to Find Them.

In person, she cuts a jaunty, unassuming figure. She saunters into the room in white trainers and navy trousers, red socks visible in the gap between them: a black tank-top partially conceals a white T-shirt. She is tomboyish and tall, like Ally Sheedy on stilts, so that when she folds her long legs under her chair, she looks exaggeratedly S-shaped. Dealing with the weight of expectation from Alien fans hasn’t been too intense, she says, nibbling on a pain aux raisins. “The way I looked at it with this and Fantastic Beasts was that it was like being recruited on to a sports team. There’s a devotion from these fans who are just excited for the next game. They aren’t sat there thinking: ‘You’d better not let me down, Waterston!’”

Rumours suggested that Daniels would be Ripley’s mother and, whatever the truth, there are resemblances. Both are rational women transformed by circumstance into gun-toting warriors. Both are shown at some point in singlets, or clomping around in magnetic boots, and each has a problematic relationship with a synthetic colleague. The only shortfall comes in the area of the catchphrase, where Daniels’s multiple efforts (including “I got you, you son-of-a-bitch” and “Let’s kill this fucker!”) are no match for Ripley’s emphatic: “Get away from her, you bitch!”

Most strikingly, the first note Waterston has to play in the new film is outright panic when technical problems wake her prematurely from hypersleep. The second is grief. “It’s like slamming on the brakes before anyone has the chance to buckle their seat belts. I didn’t know how I would play it or how I could get there, but that’s always the most appealing thing to me. The insecurity is exciting. Maybe I’m also curious about testing my ability.” She widens her eyes. “Seeing if it’s still there.”

Although Daniels is treading in Ripley’s footsteps, or, given that Covenant is set 20-odd years before Alien, forging the path that Ripley will follow, Waterston didn’t talk to Weaver about the part. But the two women have a distant connection. When Waterston was starting out as an actor, she got her first lead role in a play at The Flea, a New York theatre co-founded by Weaver’s husband, Jim Simpson. “Sigourney came to see it and said something like: ‘You were good.’ Nothing extraordinary. But when someone like her says that, you hang on to it for years. When I got this job, I thought immediately of that moment.”

Waterston is big on the idea of all actors as an extended clan, perhaps unsurprisingly for someone whose siblings are in the business, and whose father is Sam Waterston, the veteran from The Killing Fields, Crimes and Misdemeanors and the TV hit Law and Order. Her mother is the former model Lynn Louisa Woodruff. “Acting is a community where you come in and out of each other’s lives. I’m slightly envious of the golden age of Hollywood. It must have been frustrating to be owned by the studio, but it was also like being in a company, working with the same people, and that appeals to me.”

Working On Alien: Covenant, she was reunited with Carmen Ejogo (Fantastic Beasts) and Michael Fassbender, with whom she shared some fraught scenes in Steve Jobs, as well as her old chum Billy Crudup. At one point during our conversation, she leaps up and yanks open the door in response to voices outside. “Billy Crudup, will you shut the fuck up?” she hollers down the hallway. “I’m trying to focus!”

Crudup sidles into view. “What you doing for dinner tonight,” he purrs. “You want to join us? Me and Danny McBride? You should be so lucky!” What larks. Of course, it’s entirely possible that she could have put on a more vivid display of her need to cultivate actorly intimacy than bounding out of the room to accost a colleague. Possible, yes, but not likely.

She first saw Crudup when she was 15 in a Broadway production of Tom Stoppard’s Arcadia, which she now credits with confirming in her mind her acting ambitions. “It was the thing that clicked me over to that next level of curiosity.” Clicked? “You know when you’re going up at the start of the rollercoaster and it’s going click-click-click towards the summit? I’d had the initial idea of wanting to act but I didn’t know how I could do it.”

Even though her dad is an actor? “I know! Isn’t that weird?” On a rollercoaster, there’s an inevitability about what’s going to happen next.

Did acting feel that way? “Yes. Even though I wasn’t sure how it would come about, I knew it would.”

Determined to distinguish herself from her family, she eschewed performing as a teenager. Didn’t appear in so much as a school play. Photography was her bag. “I loved the darkroom. It’s a good place for an angsty teenager.” Her favourite picture is one she took while visiting her father on location in Dublin. “It’s of this drunk gambler at the racetrack, totally loaded, who had climbed into a tree to get a better view of the horses.” She smiles sadly. “I can’t imagine having the guts to do that now. I wonder sometimes if I’ve got in the habit of only being courageous when someone else has written the words I have to say.”

No one who gave the sort of performance that Waterston did in Inherent Vice should be in any hurry to sell herself short. Shasta Fay appears in only a couple of scenes but her presence permeates the film; she is the personification of its riddles. Attention at the time focused disproportionately on one scene in which Waterston lies naked across the lap of her ex-lover, played by Joaquin Phoenix, and invites him to spank her. “One journalist asked if Joaquin left red marks on my butt,” she recalls incredulously. “I wish I’d said: ‘I don’t remember but I’ll tell you what – bend over and I’ll spank you as hard as I can and we’ll see what happens.’

“We live in such hypersexualised yet totally prudish times. People have this expectation about everyone else’s relationship to their own bodies. ‘Surely you must have shame about your body? Surely what’s scariest for you as actor would be to stand in a room naked?’ Believe me, I’ve been in so many more terrifying situations as a performer than that. This was working with people I trusted in a scene that was rich and complex and there was so much to do there that I hardly even thought about that thing that seems to be all everyone could talk about. They’re just hoping I’ll say: ‘Oh, I was so scared that day and then I drank a few shots of whisky and I felt better.’” She gives a mighty roll of the eyes.

After Inherent Vice wrapped, she was convinced she would become known as the first actor to be bad in an Anderson movie. “That period between finishing the film and opening night is agonising. That’s part of why actors go from job to job – so they don’t have to live with the anxiety in the interim.”

As if to prove that, she has already shot another three pictures since Alien: Covenant, including Steven Soderbergh’s Logan Lucky opposite Channing Tatum, and is about to start Fantastic Beasts 2.

Having likened acting to a sports team and a rollercoaster, she saves her most conflicted analogy for last. “I’ve heard this is how cults brainwash people,” she says. “You wake up and you go to conferences that go on all day and then you’re so exhausted that you sleep, and then you get up and do it again the next day. That’s what it’s like making movies. You’re up before dawn, you collapse at night and then you do it all over again until there’s no room for anything else in your brain.”

• Alien: Covenant is released in Australia today, in the UK on 12 May, and the US on 19 May.