Pryma began competing internationally in 2006 but only participated in junior competitions.

He debuted at World Cup on 14 January 2010, in German Ruhpolding, where he was 41st in the sprint.

At 2011 Winter Universiade in Erzurum, Turkey, he won four medals, including two gold.

Together with Serhiy Semenov and Vita Semerenko, they were the most successful biathletes at those competitions.

Roman Pryma, a former biathlete and current coach, is Artem's elder brother.