Jelley began his career in Formula Ford before graduating to the National Class of the British Formula 3 Championship in 2004, where he took three class wins. He drove for Räikkönen Robertson Racing in British F3 in 2006 and 2007, finishing third overall in the 2007 season after claiming two wins and a second place in the opening round. His single-seater path continued with a campaign in the 2008 GP2 Asia Series for the ART Grand Prix team.
Jelley switched to touring cars following his GP2 Asia campaign, joining the 2008 British Touring Car Championship with Team RAC as team-mate to Colin Turkington. The dual-programme commitment created scheduling pressure when a GP2 Asia weekend in Dubai fell on the same weekend as BTCC qualifying at Rockingham, requiring Jelley to race in Dubai on the Friday and qualify in England on the Saturday.
Early results were modest — just a single point in the first four rounds — but form improved steadily through the second half of the year. At Silverstone he qualified seventh, only to dislocate his shoulder in a crash in the second race; he nonetheless competed in the third race to score points. At the Brands Hatch season finale he claimed pole position for a race, a result the team initially attributed to a timing error before confirming it.
In 2009, Jelley returned with Team RAC and converted the experience of his debut year into tangible results. He scored his first BTCC podium finishes at Croft with two second-place results and a third in the same race weekend. He then backed that up at Rockingham with two outright victories — race one from fourth on the grid and race three also from fourth — marking the high point of his early touring-car career.
Jelley moved to the British Porsche Carrera Cup with Team Parker Racing in 2010, taking 11 podium finishes including wins in the final two races of the season. He finished third in the championship behind Tim Harvey and Michael Caine.
He remained with Team Parker for 2011 — a late decision after an initial agreement to contest the Le Mans Series fell through. Jelley took pole for the first two rounds at Brands Hatch and won the second race from pole. He competed for the title against the SAS-backed cars of James Sutton and Michael Meadows, entering the final meeting of the year level on points with his rivals before a fuel pick-up problem in qualifying compromised his championship push. He recorded five wins across the season. Autosport Magazine highlighted his overtaking performances, noting he gained more positions in-race than any other driver in the series that year.
Alongside the 2011 Carrera Cup campaign, Jelley drove in two British GT Championship rounds for Trackspeed Racing in a Porsche GT3R alongside David Ashburn, claiming pole position for the Donington 3-hour event. In 2012 he contested three British GT rounds with Motorbase Performance in a Porsche GT3R, partnering businessman Steve Parish, and claimed pole at both Rockingham and Brands Hatch.
During 2012 Jelley also drove for Von Ryan Racing in the Blancpain Endurance Series in a McLaren MP4-12C GT3, sharing the car with brothers Matt and Julien Draper. That programme included the Spa 24 Hours.
After two further seasons in the Porsche Carrera Cup, Jelley rejoined the BTCC in 2017 with Team Parker Racing driving a Ford Focus. The team struggled for pace and scored only two points across the season. For 2018 the team switched to an ex-WSR BMW 125i, and while results remained difficult, Jelley's strongest performance came at Knockhill where he qualified second and ran in that position until contact from former team-mate Colin Turkington ended his race.
Continuing with Team Parker and BMW into 2019, Jelley immediately found better form, taking a podium in race three at the opening Brands Hatch round. Later in the season he crossed the line first in race three at another round, only to be classified runner-up after a 20-second penalty was applied to the original race winner, promoting him from second to first officially.
He raced in the BTCC through the 2023 season, after which he confirmed his departure from West Surrey Racing.
Ahead of 2024, Jelley returned to the British Porsche Carrera Cup with Team Parker Racing. For the 2025 British Touring Car Championship he joined One Motorsport, driving a Honda Civic Type-R alongside Josh Cook.