Čebašek ran for the first time in January 2006 in Ortisei am Pillersee in the Alpencup and took 55th place over 5 km classic. She ran her first World Cup race in December 2009 in Rogla , which she finished in 56th place in the sprint. In the 2010/11 season she achieved her first podium finishes in the Alpine Cup with two second and two third places and thus achieved ninth place in the overall standings. She won her first World Cup points in Rybinsk in February 2011 with 13th place in the sprint. At the Nordic World Ski Championships in Oslo in 2011 , she finished 46th over 10 km classic and 19th in the sprint. In February 2012 she reached 12th place in Szklarska Poreba , her best individual World Cup result to date. The following month she won her first Alpine Cup victories in Rogla and Toblach . She also came third twice and was eighth in the overall ranking of the Alpine Cup . At the Nordic Opening in Kuusamo at the beginning of the 2012/13 season, she finished 63rd. In the further course of the season she achieved four podium placements, including a win in the Alpine Cup and thus achieved 13th place in the overall Alpine Cup ranking. Her best results at the Nordic World Ski Championships 2013 in Val di Fiemme were 37th place in the sprint and 14th place in the relay. After finishing 31st at the Nordic Opening in Kuusamo at the beginning of the 2013/14 season, she made it into the points eight times in the World Cup. In the Tour de Ski 2013/14 , which she did not finish, she achieved her best individual result in the World Cup with eighth place in the prologue race. Her best results at the 2014 Winter Olympics in Sochi were 17th place in the sprint and tenth place in the team sprint. In March 2014 she won her fourth Alpine Cup victory in Valdidentro . She ended the 2013/14 season in 55th place in the overall World Cup ranking. In the following season she came in the points 15 times in the World Cup, including 24th place at the Nordic Opening in Lillehammer . In the 2015/16 season she took 39th place at the Nordic Opening in Ruka and 30th place at the Ski Tour Canada . Her best individual placement of the season in the World Cup was tenth place in the 5 km stage in Ruka. In the following year, at the Nordic World Ski Championships in Lahti in 2017 , she finished 39th in the skiathlon, 18th in the sprint and 13th place in the relay. In the 2017/18 season she took 55th place in the Ruka Triple and 51st place in the World Cup final in Falun . Her best results at the 2018 Winter Olympics in Pyeongchang were 12th place over 10 km freestyle and sixth place together with Anamarija Lampič in the team sprint.
In the 2018/19 season, Čebašek took 35th place in the Lillehammer Triple and 21st place in the 2018/19 Tour de Ski , making it 34th in the overall World Cup. At the season highlight, the Nordic World Ski Championships 2019 in Seefeld in Tyrol , she ran to 36th place in the skiathlon , 27th place in the sprint and ninth place with the relay.