Vips began competitive karting in 2011 in Estonia. He won the Rotax Junior Estonian Championship in 2013 and claimed victory at the 2014 Rotax Max Challenge Grand Finals in the Junior category. His karting campaigns brought him into early contact with drivers who would become future FIA Formula 3 peers, including Richard Verschoor and Marcus Armstrong, when he competed in the CIK-FIA European KF1 Championship in 2015, finishing twelfth.
Vips made his car-racing debut in 2016 with Prema Powerteam, competing in both the Italian F4 and ADAC Formula 4 championships. He finished fifth in Italian F4 — taking a race win at the final round and claiming the rookie title — and sixth in ADAC Formula 4. Over the winter of 2016–17 he raced in the MRF Challenge Formula 2000 Championship in India, collecting three podiums. Returning in 2017, Vips took the ADAC Formula 4 title in a straight fight with teammate Marcus Armstrong, clinching it in the final race at Hockenheimring after the pole-sitting Armstrong lost the lead to Artem Petrov.
Following his Formula 4 championship, Vips tested Formula 3 machinery with Prema at Magny-Cours in September 2017 and made a brief guest appearance in the FIA Formula 3 European Championship that October, replacing an absent Motopark driver.
He secured a full-time seat with Motopark for the 2018 FIA Formula 3 European Championship. The season placed him in strong company: teammate Dan Ticktum eventually won the title, while Prema entries Mick Schumacher and Robert Shwartzman claimed second and third. Vips took three pole positions and four race wins across the season and finished fourth in the championship, a result that underlined his pace even in defeat.
His first outing at the Macau Grand Prix came in November 2018. He qualified fourteenth and improved to seventh in the qualification race, only to be penalised forty-two seconds in the main race for overtaking under red-flag conditions, which demoted him from seventh to nineteenth at the finish.
For 2019, Vips moved to the newly rebranded FIA Formula 3 Championship with Hitech Grand Prix. He took feature race victories at the Red Bull Ring and at Silverstone — the latter from pole position — and a sprint race win at Sochi. He ended the season fourth in the drivers' championship, behind the three Prema drivers Robert Shwartzman, Marcus Armstrong, and Jehan Daruvala, completing a run of strong but ultimately title-less campaigns in the junior formula.
The 2019 Macau Grand Prix proved to be the defining highlight of Vips's Formula 3 years. He set the fastest qualifying time of the entire field — a new absolute lap record around the Guia Circuit — and converted pole position into a qualifying race victory, giving him pole for the main event. Leading in the early laps, his bid for the win was frustrated by safety car periods triggered by crashes from Leonardo Pulcini and Ferdinand Habsburg. When racing resumed, Richard Verschoor passed him and held on to the flag; Vips crossed the line 0.792 seconds behind in second place. The result remained a deeply creditable performance at one of motorsport's most demanding street circuits.
Vips's Formula 3 career established him as among the quickest drivers of his generation in junior single-seaters, with his Macau pole lap record standing as a benchmark performance. He subsequently progressed to the FIA Formula 2 Championship and served as a reserve and test driver for Red Bull Racing before a sponsorship incident ended that relationship in 2022. He later moved to IndyCar racing with Rahal Letterman Lanigan Racing and in 2026 made his sportscar debut in the GTD Pro class at the 24 Hours of Daytona with RLL Team McLaren.