In 2017, Kvapil ran in select events in the Southeast Limited Late Model Series as well as the Challenger Division. It was in the latter series where he won in two of three starts in the division that year, with those wins coming at Dillon Motor Speedway and
Florence Motor Speedway. In the following year, he ran select races in the
ARCA Midwest Tour, winning in his first start at Golden Sands Speedway before twentieth and fourth in his next starts at Grundy County Speedway and Dells Raceway Park respectively. He also made his
CARS Late Model Stock Tour debut that year, driving the No. 35
Chevrolet, and finished 17th at Tri-County Speedway. In 2019, Kvapil ran three races of the
CARS Super Late Model Tour and got a best finish of second at
South Boston Speedway. He also ran one Late Model Tour race at
Orange County Speedway, finishing 22nd. In 2020, he ran all but one race in the Super Late Model Tour and finished fifth in the standings with a best finish of fourth at both events at
Hickory Motor Speedway. Also in 2020, he won the Carolina Pro Late Model Series championship, winning six races despite running in only seven of the nine scheduled events. Also in 2021, he ran three
ARCA Menards Series East races for
Cook-Finley Racing in the No. 41
Chevrolet. He failed to finish all three events he entered, finishing 14th at the season-opening race at
New Smyrna Speedway due to an ignition issue, 11th at
Five Flags Speedway due to vibration, and again 11th at
Nashville Fairgrounds Speedway due to engine issues. In 2022, Kvapil joined
JR Motorsports in its
Drivers Edge Development program alongside plans to run the full Late Model Stock Tour in the No. 8
Chevrolet, replacing
Josh Berry, who ran full-time with the team in the
NASCAR Xfinity Series that year. He started off his season by winning the first race of the year at the Old State Nationals event at
Caraway Speedway after leading 59 laps. After finishes of second, third, and fourth in the next three rounds, he won at Franklin County Speedway on his nineteenth birthday. He then won the inaugural Window World 125 at
North Wilkesboro Speedway in August. Kvapil was suspended from the event at
Ace Speedway and was fined $500 after he turned
Zack Miracle into the wall on the cooldown lap of the Tri-County event. Despite this, he went on to secure the championship on his first race after his suspension with a win at South Boston and finished third in the final race of the year at Caraway. In 2023, Kvapil won his second straight Late Model Stock Tour championship, getting five wins and finishing in the top ten in all but one race that year. It was also during this year that he returned to ARCA, this time making his debut in the main ARCA series, driving the No. 28
Chevrolet for
Pinnacle Racing Group at
Kansas Speedway, where he finished in second behind race winner
Connor Mosack. He also made his debut in the
NASCAR Craftsman Truck Series driving the No. 7
Chevrolet for
Spire Motorsports at
Bristol Motor Speedway, where he started in 27th but went on to finish in twelfth. in 2024. On February 22, 2024, it was announced that Kvapil would attempt to make his
NASCAR Xfinity Series debut at
Martinsville Speedway, driving the No. 88
Chevrolet for
JR Motorsports. Kvapil impressed from the start finishing in fourth place. Three weeks later, in just his second career Xfinity Series start, Kvapil was in position to win at
Dover Motor Speedway and led fourteen laps of the race in the closing laps, but ultimately finished in second behind
Ryan Truex at the end of the race. in 2025 On October 1, 2024, it was announced that Kvapil would run full-time for JRM in the Xfinity Series in 2025, driving the No. 1
Chevrolet and replacing
Sam Mayer who moved to
Haas Factory Team. Also during 2025, Kvapil competed for
CR7 Motorsports in the
NASCAR Craftsman Truck Series, driving the No. 97 truck at
Richmond. On September 24, 2025, it was announced that Kvapil will drive the No. 1 car part-time for the 2026 season, sharing with
Connor Zilisch. However, on October 29, 2025, JRM clarified that Kvapil will continue driving full-time for them. On April 18, 2026, during the
2026 Kansas Lottery 300, Kvapil was involved in a major crash on lap 2. As the caution was being thrown for an incident involving
Josh Bilicki and
Kyle Sieg, Kvapil was clipped in the left rear by
William Byron. The contact sent Kvapil spinning into the wall and into the path of
Parker Retzlaff. The collision with Retzlaff allowed enough air to get underneath his car, flipping it onto its roof. Kvapil's car slid on its roof before flipping once and coming to a stop upside down. After the red flag was thrown, Kvapil was flipped back onto all four wheels by safety crews, Kvapil got out of the car under his own power, and was released from the infield care center shortly after. ==Personal life==