Opting to continue with professional career, and in his first full season with Dynamo Pardubice in 2017–18, Kaut improved his overall impact, showing a strong two-way ability in scoring 9 goals and adding 7 assists for 16 points as the youngest player on the team's roster.

Kaut's standout play in the Extraliga playoffs and World Juniors led to a rise in the winger's draft stock, climbing from eleventh on the NHL Central Scouting Bureau International skater ranks to finishing the year fourth on the list.

[6] In leaving the Czech Republic, Kaut attended his first training camp with the Avalanche in 2018, and quickly adapted to the North American game through the pre-season, playing in contests alongside Tyson Jost and Alexander Kerfoot.

[7] Eligible to continue his development in the American Hockey League due to his European status, Kaut was assigned to primary affiliate, the Colorado Eagles for their inaugural 2018–19 season in the AHL on 27 September 2018.

[20][non-primary source needed] Approaching the off-season with the 2020–21 delayed North American season, Kaut remained in the Czech Republic, loaned by the Colorado Avalanche to resume playing with former club, HC Dynamo Pardubice of the ELH on 12 September 2020.

[23] With his initial loan agreement set to expire in early November and with the need to continue to play, Kaut was reassigned by the Avalanche, leaving Dynamo Pardubice to join Swedish HockeyAllsvenskan club, Modo Hockey, on 26 October 2020.

[25] Approaching his fifth year within the Avalanche organization in the 2022–23 season, Kaut failed to make the opening night roster and was familiarly re-assigned after clearing waivers to AHL affiliate, the Colorado Eagles.

On 25 January 2023, while on assignment with the Eagles, Kaut's tenure with the Avalanche ended as he was traded alongside Jacob MacDonald to the San Jose Sharks in exchange for Matt Nieto and fellow 2018 first-round pick, Ryan Merkley.

[1] Kaut emerged as a standout at the 2018 World Junior Championships in Buffalo, New York, where he ranked fourth on the team with 7 points in 7 games en route to a fourth-place finish at the tournament.