Her television projects include the Showtime psychological drama series Yellowjackets (2021–present) and the Star Wars miniseries The Book of Boba Fett (2022).

The same year, she made another guest appearance in Fox's supernatural horror television series The Exorcist, where she played a younger version of Regan MacNeil.

[9] In 2018, Thatcher made her big screen debut in the science fiction film Prospect, co-starring Pedro Pascal.

For her performance, she received mostly positive reviews, with Peter Debruge of Variety describing her as "a fresh face who tricks us into assuming she's just a callow teen, when in fact, she proves to be the film's toughest character".

Regarding the process, creator Bart Nickerson said the casting department was searching for "someone who was really free-spirited and unique who could play both a sort of wildness and a vulnerability."

[16] Yellowjackets premiered in November 2021 to rave reviews and became the second-most streamed series in Showtime's history behind Dexter: New Blood.

Thatcher next appeared alongside Chris Messina and David Dastmalchian in the horror film The Boogeyman, based on the Stephen King short story of the same name and released in theatres on June 2, 2023.

As of 2024, she lives in the Nichols Canyon neighborhood of Los Angeles with her boyfriend Austin Feinstein, musician and member of the band Slow Hollows.