“Supergirl” star Milly Alcock’s first big role outside of Australia was dragon sized.

As Rhaenyra Targaryen in “House of the Dragon” — HBO’s “Game of Thrones” prequel series that premiered in August 2022 — Alcock played the headstrong, dragon-riding princess whom her father names as his heir, causing chaos in Westeros. Alcock landed the part at age 20, auditioning remotely during the pandemic from her home in Sydney. And though she was in only the first half of the show’s first season — before Emma D’Arcy took over to play Rhaenyra as an adult — she became an immediate fan favorite.

And it was Alcock’s performance as Rhaenyra that drew the attention of James Gunn, the writer-director of “Superman” who, with Peter Safran, also runs DC Studios as co-chairmen and co-CEOs. Gunn, Safran and the DC team cast Alcock to play Kara Zor-El, known to the world as “Supergirl,” in a tag at the end of last summer’s “Superman,” the official movie kickoff of the DCU. “Supergirl” — led by Alcock in her first film role, directed by Craig Gillespie and written by Ana Nogueira — opens on June 26.

In an in-depth interview conducted in mid-April for Variety’s May 20 cover, before either of us had seen “Supergirl,” Alcock recounted her journey to playing Kara. She also delved into why she became an actor in the first place, how “House of the Dragon” changed her life — and how she’s trying to put the phone down and ignore the trolls.