Allison was born in Salisbury, North Carolina on June 25, 1992, and attended and graduated from West Rowan High School. He began racing at the age of five, competing in go-karts whilst working at his father's race shop.
Allison competed in the Allison Legacy Series from 2006 to 2013, winning the championship in 2010. He also ran in the PASS National Championship Super Late Model Series and the PASS South Super Late Model Series, as well as the X-1R Pro Cup Series.
In 2013, Allison made his ARCA Racing Series debut at the Kansas Lottery 98.9 at Kansas Speedway driving the No. 88 Ford for Team BCR Racing, where he started and finished eleventh. For 2014, Team BCR Racing announced that Allison would run in a select number of races during the 2014 season, driving the team's No. 88 entry as a teammate to the team's main driver Grant Enfinger.
At the season opener at Daytona International Speedway, Allison started twelfth but finished thirty-sixth due to being caught up in a multi-car crash on the 12th lap. He withdrew from the second round at Mobile International Speedway, then finished 19th at Talladega Superspeedway, one lap down. At Toledo Speedway, he secured his first top-ten finish with a seventh-place finish after staying out early during an early caution period and after making a late pit stop on lap 130.
Allison qualified a career best third at Pocono Raceway, having participated in a test a few days prior where he recorded a speed of 168.425 mph, and finished in fifth place, his first top-five finish. He improved on that result at Michigan Speedway, where he finished in third place behind Mason Mitchell and race winner Austin Theriault. At Chicagoland Speedway, he started and finished eighth.
On August 1, 2014, Allison returned to Pocono Raceway and started fifth. He pitted on lap 16, taking the lead after Brennan Poole and Justin Boston pitted, satisfying ARCA's rules that drivers must pit at least once before the halfway point of the race. He held off Will Kimmel to score his first career ARCA Racing Series win by four-tenths of a second. This made him the third member of the Allison family to win an ARCA Racing Series race, and the first by an Allison in a major stock car series event since Davey Allison won the Pontiac Excitement 400 at Richmond International Raceway in 1993.
Allison's last race of 2014 was at Kentucky Speedway, where he finished seventh on the lead lap after starting ninth. His final start was at the season finale at Kansas Speedway, driving the No. 08 Ford in a car that he owned, as his normal ride was occupied by Charles Evans Jr. for the event. After starting 33rd and last due to qualifying being rained out, he avoided many accidents to finish in ninth place, one lap down behind race winner Spencer Gallagher. He has not run in ARCA, or any other major stock car series, since 2014.