Bristol City 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. She went on to feature in three of
Bristol's
Spring Series games in 2017. This led to more first team opportunities in the
2017–18 season. On 12 October 2017, she made her season debut coming on as a 19th-minute substitute for
Poppy Wilson in Bristol's 2–0
WSL Cup defeat by
Tottenham. On 28 October, she made her first league start of the campaign, in a 5–0 defeat by Reading. 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.
Manchester United 2018–19 season On 1 July 2018, Palmer joined the newly formed
Manchester United to compete in the
FA Women's Championship, reuniting with manager
Willie Kirk who had been appointed assistant manager at United. 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. On 9 September, Palmer made her
Championship debut in a 12–0 win against
Aston Villa, coming on as a substitute in the 64th minute for
Lauren James. She scored her first ever senior goal on the final day of United's title winning
2018–19 season in a 5–0 victory over
Lewes.
2019–20 season: Loan to Sheffield United On 21 August 2019, Palmer joined
Sheffield United in the
FA Women's Championship on loan for the season. On 25 August, Palmer scored a brace and provided an assist on her debut as part of a 7–1 victory over
Leicester City. On 23 January 2020, Manchester United recalled Palmer. At the time of her departure, Palmer ranked as Sheffield United's fourth-highest goalscorer across all competitions. She left Manchester United following the expiration of her contract at the end of the season.
Return to Bristol City On 2 July 2020, Palmer rejoined Bristol City, signing a two-year contract with the club. She made her second debut in a 4–0 league loss to
Everton. 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.
Leicester City On 1 August 2023, Palmer joined
Women's Super League team
Leicester City on a one-year contract after winning the Championship with Bristol City.
Southampton On 6 August 2024, Palmer joined Women's Championship side
Southampton. == International career ==