Gray is the grandson of funny car and Pro Stock champion Johnny Gray, who was also president of Marbob Energy, the New Mexico oil producer his father co-founded. When Tanner's family sold the company in 2010 for $1.7 billion in proceeds, the family relocated from New Mexico to Mooresville, North Carolina, so that his father Shane Gray could pursue a full-time NHRA career. His younger brother Taylor Gray also became a NASCAR driver, competing full-time in the NASCAR O'Reilly Auto Parts Series for Joe Gibbs Racing. Since 2021, Johnny Gray has been a co-owner of Tricon Garage, the team Tanner drives for in the Truck Series.
Gray began competing in the NHRA Pro Stock class in 2017 alongside his father Shane Gray. On April 2, 2017 — thirteen days before his eighteenth birthday — he won the final round of the Denso Spark Plug Nationals at Las Vegas Motor Speedway against Bo Butner. At 17 years, 11 months, and 18 days old, he broke the record held for 40 years by Jeb Allen, who had been 18 years, 1 month, and 8 days when he set the mark. Gray won the 2017 Auto Club Road to the Future Award, given to the top rookie across all NHRA pro categories including Top Fuel, Funny Car, and Pro Stock Motorcycle.
In 2018, Gray dominated the Pro Stock class, winning eight times to claim the NHRA season championship and become the youngest-ever NHRA solo season champion.
In September 2018, Gray announced he would race in the NASCAR K&N Pro Series East for DGR-Crosley in 2019 after meeting team owner David Gilliland. He picked up his first K&N win at South Boston Speedway in May 2019. In 2020, Gray ran part-time in the ARCA Menards Series, sharing the No. 17 car with his younger brother Taylor and Anthony Alfredo. He returned to ARCA for select races in 2021 and 2024, the latter with Joe Gibbs Racing's No. 18 at tracks 1.5 miles and longer where younger JGR driver William Sawalich was ineligible due to age.
Gray made his Truck Series debut in October 2019 at Martinsville Speedway with DGR-Crosley, running the No. 15 Toyota Tundra. He extended his schedule to include ISM Raceway and Homestead-Miami Speedway that same season. For 2020, DGR-Crosley moved Gray to the No. 15 Ford F-150 after switching from Toyota, running him full-time and as a rookie. He earned eight top-ten finishes and four top-fives, finishing fourteenth in points and fifth in Rookie of the Year standings.
Gray returned to the team in 2021 under the new name David Gilliland Racing, but the season was difficult, yielding only two top-tens and an eighteenth-place points finish. He improved significantly in 2022, including three consecutive top-ten finishes to open the year, finishing 15th in points.
When David Gilliland Racing rebranded as Tricon Garage and aligned with Toyota Racing Development for 2023, Gray remained on the roster. He started the season with a career-best second-place finish at Daytona, trailing only winner Zane Smith, and scored his first career pole at Charlotte Motor Speedway at 180.385 mph. He finished fourteenth in points.
Tricon Garage renewed Gray's contract for 2025, continuing his tenure with the team he has competed with since his debut.
Gray developed his early racing skills in Mini Outlaw Karts at Millbridge Speedway in Salisbury, North Carolina, competing alongside Kyle Larson and Rico Abreu on Wednesday nights.