Eliassen has been taking part in competitions organized by the Fédération Internationale de Ski since 2003 . From 2006 to 2012 he mainly competed in the Scandinavian Cup, which he finished in sixth place overall in 2010 . At the U23 World Championship in 2008 in Mals , he won bronze over 15 km classic. He ran his first World Cup race in March 2009 in Trondheim , which he finished with 21st place in the 50 km mass start and was thus able to win his first World Cup points. In March 2010 he took second place in the relay in Lahti, his first and so far only podium in the World Cup. At the Nordic World Ski Championships in Oslo in 2011 , he finished 15th in the 15 km classic and eleventh place in the 50 km mass start race. In April 2011 he won the Saami ski race over 90 km freestyle. The strongest World Cup season to date was 2012/13 . After a weak race at the start of the season with 41st place over 15 km freestyle, he was able to win points in all World Cup races. At the Nordic World Ski Championships in 2013 in Val di Fiemme , he finished 14th in the 50 km mass start race. At the end of the season he achieved his best individual World Cup result to date with fourth place in the 50 km mass start race in Oslo. He finished the season in 35th place in the overall ranking and 24th in the distance ranking. In February 2015 he won the König-Ludwig-Lauf and in March 2015 the Wasalauf , the Birkebeinerrennet and the Årefjällsloppet . He won the overall ranking of the Ski Classics 2014/15 . In April 2015 he won the Saami skirace ski marathon over 90 km freestyle from Enontekiö to Kautokeino . In the 2015/16 season he won the Jizera Mountains Run , La Diagonela and Kaiser Maximilian Run . He also took second place at Marcialonga and Toblach – Cortina and third place at Birkebeinerrennet and Årefjällsloppet. As in the previous year, he won the overall ranking of the Ski Classics . In April 2016, like last year, he won the Saami ski race over 90 km freestyle. At the beginning of the 2016/17 season, he won the Ski Classics Prologue in Pontresina and took third place at La Sgambeda . In the further course of the season he took second place in the Toblach – Cortina, the Isergebirgslauf and the Birkebeinerrennet. At the end of the season he won the Reistadløpet and the Ylläs – Levi and came second in the overall ranking of the Ski Classics 2016/17 .
In the 2018/19 season, Eliassen triumphed at the Kaiser-Maximilian-Lauf , Marcialonga and the Birkebeinerrennet , taking second place in the overall ranking of the Ski Classics 2018/19 . The following season he won the Wasalauf. He also came third at the Marcialonga and the Jizera Mountains and second at La Venosta and Toblach – Cortina and thus achieved fourth place in the overall ranking of the Ski Classics.