Juri Vips began competing professionally on the karting scene in 2011, claiming major titles in his native Estonia and the Rotax Max junior championship. 2014 year began with victory in Rotax Winter Cup in Spain and later in the year Vips came a champion in Rotax World in Valencia Junior Class.

In 2016, Vips made his single-seater debut in the Italian F4 and ADAC Formula 4 championships with Prema Powerteam, where he claimed a victory and took the title of Italian F4 rookie champion in 2016.

In 2017, Vips continued with Prema in both championships, claiming the ADAC Formula 4 title ahead of teammate Marcus Armstrong. In 2017, Vips tested the machinery with Prema.

For the 2018 season, Vips drove for German team Motopark, claiming four wins and taking fourth in the driver’s championship. In 2019 Vips joined Hitech GP and Red Bull Junior Team.

In 2020 Vips was supposed to drive for Team Mugen in the Super Formula Championship, but due to Covid-19 pandemic and related travel restrictions, he could not participate. After a few races in Formula Regional Championship, Vips had a chance to drive in FIA Formula 2 Championship, completing 8 races with DAMS and claiming 1 podium.

In November 2020, Vips received his FIA Super Licence after completing a 300km test for Red Bull, driving the Red Bull RB8 at the Silverstone Circuit. He was a reserve driver for Red Bull and sister team AlphaTauri at the last three Grand Prix weekends of 2020 F1 season. Vips tested the current Red Bull Racing RB16 at the end-of-season young driver test that took place week after the 2020 Abu Dhabi GP.

In 2021 & 2022, Jüri raced in FIA Formula 2 championship, where he had 3 wins and 11 podiums, finishing the season in 6th place & 11th place overall, respectively. Also, he had his second career F1 young drivers test after the season finale Abu Dhabi race.

In 2023, Juri tested in the NTT INDYCAR SERIES with Rahal Letterman Lanigan Racing, and joined the team for the final two races of the 2023 season.