Interested in acting from a young age, she did some modeling as a teenager to save money to move to London.

In 2015, she was set to star in a TV adaptation of the novel The Clan of the Cave Bear; however, Lifetime cancelled the series before it ever went into production.

In 2020, she starred in two miniseries: White House Farm on ITV as Sally Jones and Roadkill on BBC One as Lily Laurence.

Brady made her Off West End debut in February 2022 appearing in an English-language translation of the play The Forest by Florian Zeller at the Hampstead Theatre, directed by Jonathan Kent.

[16] In August 2022 it was announced that Brady would star as the lead in the Filip Jan Rymza-directed feature film Object Permanence, playing "Brooke Brooks, a former supermodel who becomes a highly successful lifestyle mogul and the first person to IPO (Initial Public Offering) herself."