In the summer of 2020, Chukste signed a contract with the San Jose Barracuda of the American Hockey League.

The first part of the season was played by Riga "Dinamo,"  but it ended with the Finnish team Pelicans Lahti.

In the season of 2008, he represented the Czech Extraliga club Oceláři" of Tršinec, winning the championship title.

Čukste initially was included in the Latvian national team for 2022 Winter Olympics but was withdrawn from the squad on the day of departure due to a positive COVID-19 test.

Čukste also played for the Latvian national team at the 2023 World Championship and won a bronze medal.