[3] He competed in the CIK-FIA European KF1 Championship in 2015, racing against future FIA Formula 3 competitors Richard Verschoor and Marcus Armstrong.

He finished sixth in ADAC Formula 4 and fifth in Italian F4, where he won the final race of the season and took the title of rookie champion.

[4][5] In the winter of 2016–17, Vips took part in the Indian-based MRF Challenge Formula 2000 Championship, taking three podium places and finishing sixth in the standings.

[6] His appearances in Italian F4 were as a guest driver and he was ineligible to place in the championship, however he took two pole positions and a race victory at Mugello.

[10] He took three pole positions and four race wins on his way to fourth place in the championship, behind teammate Dan Ticktum and Prema drivers Mick Schumacher and Robert Shwartzman.

He maintained his position in the main race, finishing seventh, but was handed a 40-second time penalty for making an overtake under red-flag conditions, demoting him to nineteenth place.

[11] In December 2018 it was announced that Vips would compete in the new FIA Formula 3 Championship, joining Hitech Grand Prix for the 2019 season.

He ended the season fourth in the drivers' championship, behind the three Prema entries of Robert Shwartzman, Marcus Armstrong and Jehan Daruvala.

[14][15] Vips led in the early part of the race, but crashes from Leonardo Pulcini and Ferdinand Habsburg nullified his lead as the safety car was deployed.

[16] In October 2019, it was announced that Vips would replace Patricio O'Ward at Team Mugen for the final round of the 2019 Super Formula Championship.

However, he stalled the car during his pit stop, losing around half a minute while sat stationary and causing him to drop to eighteenth by the finish.

[20][21] However, the start of the Super Formula season was postponed until August due to the COVID-19 pandemic, and the closure of Japan's borders to foreign nationals put Vips' ability to compete into doubt.

[22] In June 2020, Vips took part in a Formula Regional European Championship (FREC) test at Imola with the Finnish KIC Motorsport team.

[23] Vips' manager Marko Asmer clarified that his Super Formula campaign was the priority, but that FREC would be a "back-up" if travel to Japan became impossible.

[25][26] Shortly after claiming a double podium finish in the FREC round at Circuit Paul Ricard, Vips was called up to the FIA Formula 2 Championship to replace injured DAMS driver Sean Gelael.

[29] This caused him to miss the fifth and sixth rounds of FREC, limiting his chances of earning FIA Super Licence points through that series.

[30] In January 2021, it was announced that Vips would make his full-time Formula 2 debut, contesting the 2021 season with Hitech Grand Prix alongside Liam Lawson.

[34] At the third round at the Baku City Circuit, Vips qualified a season best 2nd, locking up a Hitech front row alongside Lawson on pole.

He served as a reserve driver for Red Bull and sister team AlphaTauri at the Turkish, Bahrain, Sakhir and Abu Dhabi Grands Prix.

He made his Formula One free practice debut with Red Bull at the 2022 Spanish Grand Prix, taking Sergio Pérez's place.

[46] In June 2022, Vips was suspended by Red Bull pending an investigation after he was heard using the word "nigga" while playing a video game on his teammate Liam Lawson's Twitch livestream.

[50] On July 6, Christian Horner, Red Bull's team principal, made some statements that implied that they would continue to support Jüri Vips "from a mental health and educational perspective" since "everybody at some point deserves a second chance" and that he would continue in the Red Bull Junior Team, even if his contract as a reserve and test driver was terminated.

[53][54] In October 2022 Vips took part in a private IndyCar driver evaluation test at Sebring with Rahal Letterman Lanigan Racing.

[56] On 13 March 2023, Vips participated in a second IndyCar test with Rahal Letterman Lanigan Racing at Barber, replacing Jack Harvey who was deemed unfit following an injury at the Grand Prix of St.