Palmer broke into the first-team making her senior debut in the WSL 1 on 22 April 2017, as a substitute for Jasmine Matthews in a 3–1 loss to Reading.

[5] While training with Bristol City, Palmer studied for her A levels in psychology, biology and chemistry at SGS College and was named Student of the Year.

[8][9] She made her competitive debut for Manchester United, as a 61st minute substitute for Mollie Green, in a 2–0 League Cup defeat against Reading on 25 August.

[17] Palmer was in the first team in January 2023 when Bristol won a 4–0 victory over Oxford United to join the 5th round of the women's FA cup.

[22] On 3 April 2018, Palmer scored on her under-19 debut as England beat Israel 4–1 in an elite round qualifying game for the 2018 UEFA Women's Under-19 Championship.

[23] Four months later, in the opening round of qualifying for the 2019 tournament, Palmer scored braces in consecutive games as England eased past Malta and Croatia, 9–0 and 8–0 respectively.