Levick played club cricket for Upper Haugh Cricket Club in Rotherham, alongside her brother.[1][2] The club had no girls team, so she played on the boys team.[2] At the age of 16, Levick debuted for Yorkshire Women.[1] She has taken 190 wickets in the Women's County Championship, more than any other player.[1][4] Levick took 20 wickets in the 2015 season at an average of 9 runs per wicket. She was the second highest wicket taker in the competition, behind Sarah Clarke.[5] In 2018, Levick took 20 wickets for Yorkshire Women in the County Championship and Twenty20 tournaments.[6]
From 2011 to 2012, Levick was a member of the England Academy squad, but after graduating from university, she left the academy to find paid work.[1] Levick played in the Women's Cricket Super League between 2016 and 2019, representing the Yorkshire Diamonds.[2] She took 29 wickets, more than any other non-international cricketer, at an economy rate of 6.60.[1][2] In 2019, Levick was named The Guardian's Women's Cricketer of the Year.[1][4]
In 2020, Levick played for the Northern Diamonds in the Rachael Heyhoe Flint Trophy.[4] She took eight wickets in the group stages of the tournament,[7] including taking 3/22 from 10 overs in the Diamonds' match against North West Thunder.[8] In the Rachael Heyhoe Flint Trophy final against Southern Vipers, Levick took 3/49 from 8 overs, including the wicket of Georgia Adams.[9] Levick signed for the Northern Superchargers for The Hundred.[2] The 2020 season of The Hundred was cancelled due to the COVID-19 pandemic,[3] but Levick was retained by the Superchargers for the 2021 season.[10] In October 2020, Levick tested positive for COVID-19, and later suffered the effects of long COVID. At one point, she was unsure if she would be able to play cricket again, though she later returned to action in the 2021 Rachael Heyhoe Flint Trophy.[11] At the end of the 2021 season, it was announced that Levick had signed a professional contract with Northern Diamonds.[12]