Kelly made her county debut in 2011, for Warwickshire against Cheshire. She scored 12 runs and bowled 2 overs for no wicket.[5] In 2012, in two innings over one weekend playing for Warwickshire Under-17s, Kelly scored 201* and 110* and soon after became a regular in Warwickshire's first team.[3] She hit her maiden T20 half-century in 2013, against the Netherlands.[6]
Kelly began captaining Warwickshire in 2015, standing-in for Rebecca Grundy. She became permanent captain of the side in 2016.[7] In 2019, Kelly led her side to victory in the Twenty20 Cup. Warwickshire topped Division 1 by one point after beating runners-up Lancashire in the final match, with Kelly top-scoring with 76.[8][3] She also ended the season as the leading run-scorer in Division 1.[9] Kelly was Warwickshire's leading run-scorer in the 2021 Women's Twenty20 Cup, with 162 runs at an average of 81.00.[10] She was again Warwickshire's leading run-scorer in the 2022 Women's Twenty20 Cup, with 192 runs at an average of 32.00.[11] She scored two half-centuries on the same day in a double-header against Gloucestershire, 99 from 61 deliveries in the first match and 60 from 27 deliveries in the second.[12][13] In the second match, her half-century came from 15 deliveries, which is the fastest recorded fifty in Women's Twenty20 cricket.[14] She played two matches for Warwickshire in the 2023 Women's Twenty20 Cup, scoring 75 runs and taking two wickets.[15][16]
Kelly also played in the Women's Cricket Super League, for Loughborough Lightning in 2017 and Southern Vipers in 2019.[2] She played one match for Loughborough, in which she scored 18 runs against Western Storm. She played five matches for the Vipers, scoring 13 runs at an average of 4.33.[17][18] In 2020, Kelly was announced as part of the Central Sparks squad for the Rachael Heyhoe Flint Trophy. She was the side's second-highest run-scorer, with 223 runs at an average of 55.75, and scored two half-centuries.[19] In December 2020, it was announced that Kelly was one of the 41 female cricketers that had signed a full-time domestic contract.[20]
In 2021, Kelly scored 182 runs for Central Sparks in the Rachael Heyhoe Flint Trophy, including two half-centuries.[21] In a Charlotte Edwards Cup match against Southern Vipers, Kelly hit 100* from 53 balls, her Twenty20 high score and first ever century, to help her side to a 6 wicket victory.[22] She also signed to play for Birmingham Phoenix in The Hundred, but only made one appearance in the competition.[23] At the end of the season it was announced that Kelly had moved to Lightning, and signed a professional contract with her new side.[24] She played eleven matches for Lightning in 2022, across the Charlotte Edwards Cup and the Rachael Heyhoe Flint Trophy, scoring 197 runs and taking six wickets.[25][26] She also played seven matches for Trent Rockets in The Hundred, scoring 40 runs.[27]