She had initially become interested in the game after playing football in a resort whilst on holiday with her family, and as a result her mother started looking for a team for Hennessy to join.
[2] Coming through the Arsenal academy, Hennessy made her unofficial first-team debut on 1 August 2021 as a 60th-minute substitute against Chelsea in a preseason friendly.
[3][4] She started in a North London Derby friendly match against Tottenham Hotspur a week later and scored twice as Arsenal won 4–0.
[5][3] Hennessy made her competitive debut on 12 September 2021 in a 4–0 FA Women's Super League win over Reading, playing the final 12 minutes.
[6] Hennessy made her debut for Crystal Palace on 30 January 2022, coming on as a substitute for the last 14 minutes in a 3–1 victory over Lewes.