She began her career in modelling, and subsequently made her screen debut as Jo March in the 2017 BBC adaptation of Little Women.

Hawke gained recognition for starring as Robin Buckley in the Netflix science fiction series Stranger Things (2019–present).

She appeared in the films Once Upon a Time in Hollywood (2019), Fear Street Part One: 1994 (2021), Do Revenge (2022), Asteroid City (2023), Maestro (2023), and Wildcat (2023), and had a voice role in Inside Out 2 (2024).

[12][13] Schlebrügge's mother, Birgit Holmquist, was also a model, having posed for Axel Ebbe's [sv] statue Famntaget, currently in Smygehuk in Sweden.

[7] Hawke also took part in summer studies at the Royal Academy of Dramatic Art in London and the Stella Adler Studio of Acting in New York.

[19] Hawke was Sofia Coppola's choice to play the title role of The Little Mermaid in Universal Pictures's live-action adaptation.

[24][25] Also that year, Hawke played Linda Kasabian/'Flowerchild' in Quentin Tarantino's Once Upon a Time in Hollywood,[26] and co-starred in Marc Meyers' thriller film Human Capital, which is based on Stephen Amidon's 2004 novel of the same name.

[31] In 2021, she also starred in a spin-off podcast series based on her Stranger Things character, Rebel Robin: Surviving Hawkins.

[37] She appeared in the Wes Anderson romantic dramedy Asteroid City (2023) which premiered at the 76th Cannes Film Festival to positive reviews.

[47][46] On March 18, 2020, Hawke released the first single "By Myself" and announced her debut album titled Blush[48] amid the 2020 Black Lives Matter protests.

[52][46] To support the release of Blush, Hawke appeared as a musical guest for the first time in her career on The Today Show in late August 2020.

[54] For her work on Stranger Things, Hawke was nominated for Outstanding Performance by an Ensemble in a Drama Series at the 26th Screen Actors Guild Awards.