Yelloly began his motorsport career in 2005 in karting, where he was active until 2008. In the winter series of the British Formula Renault, he also was the year of his debut in Formula racing and was 14th in the standings. In 2009 he joined the Hitech Junior team in the British Formula Renault and ended his first season at the 19th place overall. In the ensuing Winter Championship he was this year behind Harry Tincknell runner-up. In 2010 he stayed with his team, which ran as Atech Grand Prix from this season. Yelloly decided a race for himself and got a total of three times on the podium. At the end of the season, he finished as the second best pilot of his team behind Tamás Pál Kiss seventh place in the drivers' standings. He also began as a guest in two races in the Formula Renault 2.0 Eurocup.
2011 Yelloly Atech CRS GP went for in the GP3 Series at the start. He scored at two points race and third place was his best result. His teammates were any points. He finished the season on top of the 21 overall. In addition, he participated in the last three race weekend of the Formula Renault 3.5 for Pons Racing. He reached the finish in his first race in sixth, but was disqualified after the race, as too little fuel was in his tank. In the following race Yelloly scored three times points and a second place was his best result. As the best pilot of the team he finished 14th in the championship. For the 2012 Formula Renault 3.5 season he received a cockpit at Comtec Racing. He won the season opener in Alcaniz, and the second race on the Nürburgring. With a total of four podium finishes, he finished the season in fifth place. Against his teammate Vittorio Ghirelli he sat down with 122 to 5 points clear through.
2013 returned Yelloly back in the GP3 Series. He received a cockpit at Carlin. His best results were two second places. Unlike him, his team-mate Alexander Sims won a race, but Sims did not complete the entire season. Yelloly was sixth in the drivers' championship, and thus a prime Carlin driver. In addition Yelloly took part in a meeting of the Formula Renault 3.5 season 2013 for zeta Corse. 2014 moved Yelloly within the GP3 series to Status Grand Prix.
- 2005-2008: Karting
- 2008: British Formula Renault Winter Series (No. 14)
- 2009: British Formula Renault ( 19th place )
- 2009: British Formula Renault Winter Series (2nd place)
- 2010: British Formula Renault ( 7th place)
- 2011: GP3 Series ( No. 21 )
- 2011: Formula Renault 3.5 ( 14th)
- 2012: Formula Renault 3.5 ( 5th place)
- 2013: GP3 series ( 6th place)
- 2013: Formula Renault 3.5 (ranked 28)
- 2014: GP3 Series