Šulek started in Wisła in January 2011 for the first time in the Slavic Cup and finished 34th in the sprint and 29th in the mass start race over 12.5 km. At the European Youth Olympic Winter Festival 2011 in Liberec , he won 42nd place over 10 km classic, 35th place over 7.5 km freestyle and 20th place in sprint. At the Junior World Championships 2013 in Liberec he achieved 76th place over 10 km freestyle, 55th place in sprint and 52nd place in skiathlon and at the U23 World Championships 2014 in Fiemme Valley, 66th place over 15 km classic and 61st place Place in the sprint. In the 2015/16 season he won the overall ranking of the Slavic Cup with six top ten finishes, including two second and third places. At the U23 World Championships in 2016 in Râşnov he came in 54th place over 15 km freestyle, 38th place over 15 km classic and 31st place in the sprint. In January 2016 he completed his first World Cup race in Planica , which he finished in 71st place in the sprint. His best placement at the 2017 Winter Universiade in Almaty was 16th in the sprint and mass start race over 30 km classic. At the Nordic World Ski Championships 2017 in Lahti he ran to 64th place in the sprint and 21st place together with Andrej Segeč in the team sprint. In August 2017 he won the bronze medal in the team sprint at the Rollerski World Championships in Sollefteå together with Peter Mlynár . In the 2017/18 season he finished five times in the top ten in the Slavic Cup and thus reached sixth place overall. At the 2018 Winter Olympics in Pyeongchang , he finished 80th in the 15 km freestyle and 61st place in the sprint. In March 2018 he became the Slovak champion in the 30 km mass start race in Štrbské Pleso .