Korek made his international debut at the age of 15 in October 2010 in the FIS Cup in Einsiedeln . With places 45 and 47, however, he lagged far behind his first successes. The following year he started again in the FIS Cup in July. In Gérardmer he reached the points for the first time with 10th and 26th place. Then he started in Courchevel for the first time in the Ski Jumping Continental Cup just one day later . After finishing 56th in the first competition, Korek was disqualified in the second competition.
In the summer of 2012, Korek started again in the Continental Cup in Stams and Kranj , but again failed to score points. In January he succeeded in the second competition in Sapporo with 27th place for the first time, so that one week later he switched to the team for the ski jumping World Cup . He finally made his debut in the highest ski jumping series on January 19, 2013. With 48th place in the first and 54th place in the second competition, he clearly missed the points in both competitions. Back in the Continental Cup, he was also unable to win any further points until the end of the season.
At the Canadian Championships in Whistler in 2013 he won the gold medal on the normal hill and also achieved bronze on the large hill.
After he was able to jump back into the points in Kranj in July 2013, he switched to the Ski Jumping Grand Prix . After he missed the qualification for the individual competition in Hinterzarten , he ended up with the team in the same place in fourth place, just behind the podium. In Courchevel, too, the team achieved a very good result with fifth place. In the individual competitions, however, he again fell short of the points.