Pungertar made his international debut on October 1st, 2005 with a 35th place at an FIS competition in Oberstdorf . After further FIS races, he made his debut in the FIS Cup in Ljubno in January 2006 . After Pungertar narrowly missed the 2nd run in the first competition as 31st, he surprisingly came in sixth in the second competition. In the next two years he only competed in FIS races and the FIS Cup in Bischofshofen . Towards the end of the 2007/08 season , Pungertar made his debut in the Continental Cup in Vikersund . With places 35 and 33, he just missed the second round twice. In the 2008/2009 season, Pungertar competed several times in the FIS Cup and regularly in the Alpine Cup. In the 2009/2010 season, Pungertar only competed in the Alpine Cup. Only in Kranj did he finish 46th in the Continental Cup and third in the FIS Cup. His breakthrough came in the 2010/11 season . In Lillehammer , Pungertar was only 61st in the first competition, but already fifth in the second. After further strong performances in summer, he started regularly in the Continental Cup in winter for the first time. In Pyeongchang Pungertar won both competitions and came on the podium in three other competitions. In Willingen he was even nominated for the World Cup and finished in 45th place. Pungertar also started in the World Cup in Klingenthal , Oberstdorf and Planica , but could not qualify. In the Continental Cup, he finished fifth in the overall standings.
He won the bronze medal behind Jurij Tepeš and Jaka Hvala at the Slovenian large hill championships, which were held on October 14, 2012 on the newly built hill in Planica . Almost four weeks later, in Sochi, Russia , he was able to achieve his first World Cup points in 24th place. On February 13, 2013, he achieved his best World Cup position in an individual competition with a 15th place in the Vogtland Arena in Klingenthal . Ten days later he finished 24th on the normal hill at the 2013 World Championships in Predazzo, Italy .
In the summer of 2013 he achieved two individual podium finishes at the Grand Prix and one each with the Slovenian men's and mixed teams. He won on the large hill in Almaty in September 2013 and took fourth place in the overall ranking. After three World Cup appearances with results outside the points at the beginning of the 2013/14 season, he started the season in the Continental Cup. Second place in Brotterode was his best placement. At the end of the season, he entered the World Cup again, but could not achieve any World Cup points. After a moderate start to the 2014/15 season , he achieved his first top ten placements in the World Cup in Nizhny Tagil with places seven and six. At the following World Cup in Engelberg he came in seventh place again in the top ten. In the Four Hills Tournament 2014/15 he finished 27th. In the further course of the season he reached placements in midfield and finished the season in 25th place in the overall World Cup. At the Nordic World Ski Championships 2015 in Falun , he achieved 37th place on the large hill.