Espen Bjørnstad took part in the Nordic Junior World Championships 2013 in Liberec . There he could not win a medal, however, the best result was a sixth place in the team competition.
On March 15, 2013 he made his debut in the Nordic Combined Continental Cup . In the team sprint, which in Finnish Rovaniemi was held, he won together with Truls Johansen Sønstehagen the eighth. His best result so far in this competition series was a second place, which he was able to achieve on February 21, 2015 in a team sprint in Klingenthal together with Jarl Magnus Riiber . He achieved his best individual result on January 21, 2017 when he finished third in Otepää .
Bjørnstad made his debut in the Nordic Combined World Cup on January 4, 2014 in Tchaikovsky . In the individual competition on the normal hill, however, he had to give up prematurely during cross-country skiing. He achieved his first World Cup points on February 4, 2017 in Pyeongchang , South Korea , where he finished 29th. He achieved his first podium finishes in the 2018/19 World Cup season . In Chaux-Neuve he took second place in the Nordic Combined Triple in the first part of the competition, as well as in Lahti in the team sprint together with Jørgen Graabak . In Oslo he was third in the individual competition. Before that, he won the title with the Norwegian team at the World Championships in Seefeld on March 2, 2019 . He finished the season in ninth place in the overall World Cup standings and won the team sprint together with Jørgen Graabak at the 2019 Norwegian Championships .