Cleland came to circuit racing via autocross and hillclimb competition in the 1970s, winning his class in the Scottish Rally Championship in 1976 in a Mitsubishi Colt. He transitioned to circuit racing in the 1980s, building a strong record in British Production Car and Thundersaloon championships. In the mid-1980s his father Bill purchased the Holden VK Commodore that had finished second at the 1984 Bathurst 1000, fielded originally by Peter Brock's Holden Dealer Team, and ran it as a Vauxhall Senator in Thundersaloons for his son.
Cleland joined Vauxhall for the 1989 British Touring Car Championship and won the title at his first attempt. The championship at that time was split into separate classes competing for the same overall points table; Cleland won 11 of 13 races in the 1601–2000cc class C, dominating his category. A new 2-litre Cavalier arrived for 1990 in preparation for the single-class 2-litre era from 1991, and Cleland finished second in his class behind Frank Sytner after a season-long battle.
In 1991, under the new unified format, he won three races and finished second in the championship to Will Hoy — delivering Vauxhall its first-ever overall BTCC race win in the process. The 1992 season was similarly competitive, with Cleland battling Hoy and Tim Harvey for the title before being denied at the final round by a controversial collision with Steve Soper that handed the championship to Harvey.
BMW and Alfa Romeo dominated 1993 and 1994 respectively, and Cleland finished fourth in both years, unable to challenge the frontrunners on outright pace.
1995 proved the breakthrough year for the Cavalier, ironically in the model's final season of BTCC competition. The Volvo 850 of Rickard Rydell and the Renault Laguna of Alain Menu frequently had a speed advantage, but Cleland's ability to accumulate consistent points finishes, combined with a four-race winning streak midseason, gave him enough of a cushion to beat both rivals to the title. It was a vindication of racecraft and consistency over outright pace.
The Cavalier was replaced by the Vectra for 1996, and the new car proved problematic. Cleland fell to eighth in the standings. 1997 was worse — he slipped to twelfth as Vauxhall finished bottom of the Constructors' standings. 1998 brought some recovery, with two victories at Donington Park, but a heavy crash at Snetterton disrupted the season.
For 1999, with Vauxhall signing Yvan Muller, Cleland found himself outpaced by his new teammate. He announced his retirement mid-season, completing his final race at Silverstone in wet conditions, finishing tenth after receiving a drive-through penalty for speeding in the pits — and reacting to the stewards' decision with a characteristically unfiltered radio response that was broadcast live by the BBC.
In a 2005 Motorsport Magazine poll, Cleland was voted the tenth-greatest touring car driver of all time.
Alongside his BTCC career, Cleland competed at the Bathurst 1000 twelve times between 1993 and 2005 for various teams — Advantage Racing, Pinnacle Motorsport, Gibson Motorsport, Triple Eight, Greenfield Mowers Racing, and Brad Jones Racing. His best result was second place in the 2001 event, co-driving with Brad Jones. He also drove a Dodge Viper in the British GT Championship in 2000 with the CSi Brookspeed team, and contested an ASCAR race at Rockingham. He participated in the BTCC Masters revival race at Donington Park in 2004.
Cleland purchased his old Vauxhall Vectra Super Tourer and continued to race it in the Historic Super Touring Championship alongside contemporaries Patrick Watts and Tim Harvey. He runs a Volvo dealership in Galashiels, Scotland. After the death of fellow Scot David Leslie in 2008, Cleland became a co-commentator for Eurosport on their World Touring Car Championship coverage, working alongside Martin Haven on the English-language world feed. His son Jamie followed him into motorsport.
Cleland's two BTCC titles, achieved nine years apart with the same manufacturer, reflect unusual longevity at the front of one of Britain's most competitive championships. His combative style and refusal to concede made him a polarizing but compelling figure, and his 1995 title — clinched with consistency against faster machinery — is often cited as one of the great tactical championship campaigns of the Super Touring era.