She began her career in the film Sket (2011) and the CBBC drama Wolfblood (2012–2013), the latter of which earned her a BAFTA Children's Award nomination.

She attended Sacred Heart Catholic High School, where her English teacher persuaded her to go into performing arts when she was 11.

Kelly won a scholarship to attend Tring Park School for the Performing Arts in Hertfordshire for sixth form as a boarding student.

[2] The following year, Kelly was cast in the lead role of Madeline "Maddy" Smith in the CBBC series Wolfblood.

In 2019 and 2020, she had film roles in Armando Iannucci's The Personal History of David Copperfield and the Roger Michell's The Duke respectively.

In 2023, Kelly had a main role in the Apple TV+ thriller Hijack[8] and starred in a one-woman show adaptation of Eliza Clark's novel Boy Parts at the Soho Theatre.