2020–present: House of the Dragon
In 2020, they played Sonia Richter in the Amazon Prime Video action drama streaming series Hanna. They also starred as Astrid in the 2020 Amazon Prime Video series Truth Seekers, a comedy horror series starring Nick Frost. In March 2020, D'Arcy appeared in the comedy-drama film Misbehaviour directed by Philippa Lowthorpe. In 2021, they portrayed Emma Hobday in the romantic drama Mothering Sunday. The film was directed by Eva Husson and explored class divides and postwar survivor's guilt in 1924.
It was announced in December 2020 that D'Arcy had been cast as Rhaenyra Targaryen in the HBO fantasy series House of the Dragon, a Game of Thrones prequel and adaptation of George R. R. Martin's companion book Fire & Blood. D'Arcy admitted that while they had been aware of Game of Thrones, they had not actually seen the show until after being cast in the role of Rhaenyra. They had however read Fire & Blood. The series began production in April 2021, and its ten-episode first season debuted in August 2022. In an interview with Entertainment Weekly, showrunner and executive producer Ryan Condal revealed D'Arcy's Rhaenyra to be, in many ways, House of the Dragon's most important character, with director Miguel Sapochnik labeling D'Arcy "the face of the show." The importance of the role led to D'Arcy being placed under much scrutiny, particularly after Milly Alcock's rendition of the character in her younger years had been positively received.
D'Arcy's take on the character however was an instant hit, garnering them widespread critical acclaim with critics including it among some of the best performances of the year. In her review for The A.V. Club, critic Jenna Scherer wrote, "It's impossible to look away whenever D'Arcy's expressive face is in the frame; even when the show itself drags, they electrify every scene they're in." Writing for Comic Book Resources, Philip Etemesi pointed to D'Arcy's strong theatre background as the reason for their "expert handling of such a complex character." Additionally, Marcus Jones of IndieWire praised D'Arcy's turn as Rhaenyra, proclaiming: "Though House of the Dragon is an ensemble series, viewers can tell just by D'Arcy's presence that their Rhaenyra is the star of the show."
In November 2022, D'Arcy was honoured by GQ as one of the breakout stars of the year. They were awarded Performer of the Week by TVLine for the week of 23 October 2022, for their performance in the season one finale "The Black Queen"; TVLine later went on to name D'Arcy the year's Biggest Acting Revelation. Out magazine's Mey Rude stated, "D'Arcy has stepped up to the plate in a role that would make most actors stagger, and has become an instant star in doing so." For their performance, D'Arcy received two Golden Globe Award nominations.