Berisha was born in Egersund, and started his career in the local club Egersunds IK. He was considered as one of the biggest Norwegian talents at his age, and like his brother Valon, Veton was on a trial with Manchester City before he signed for Viking in May 2009, but didn't join the club until the summer of 2010. He made his debut for Egersunds' first-team in 2009 against Hundvåg, and in total he played 21 matches for the Third Division side.
After joining Viking, Berisha trained with the first team in the pre-season ahead of the 2011-season, and made his debut for the club when he replaced Erik Nevland after 60 minutes in the First Round of the 2011 Norwegian Cup against his old club Egersund. Berisha got his first minutes of playing-time in Tippeligaen in the 1–3 loss against Tromsø on 19 May 2011, and started his first match for Viking when Brann was beaten 3–0 on 17 June 2011.
On 19 June 2011, Berisha and his brother Valon became the first brothers to start a match for Viking in 22 years since Jan and Egil Fjetland played against Molde in the 1989 Norwegian Cup final. After the match, Viking's manager Åge Hareide said that "It's fun to start the game with two brothers, I only wish they could pass the ball to others than themselves, as it would create a lot more chances for us, but since they are brothers I guess we can forgive them. In the match against Aalesund on 17 July 2011, Berisha got his first league-goal when he scored the match-winning goal 12 minutes after he came on as a substitute to replace Erik Nevland.
During the mid-summer break in the 2012-season, Berisha expressed a concern about his lack of playing time; he had only played 69 minutes in the league that season and his last appearance in Viking's starting line-up was on 7 August 2011. But Berisha was hoping for a fresh start after Kjell Jonevret was hired as the new head coach following Hareide's departure. In the Fourth Round of the 2012 Norwegian Cup, Berisha scored Viking's first goal after only one minute on the pitch, but Brann eventually won 3–2.
On 15 July 2012, Berisha secured Jonevret his first victory as Viking-coach, when he scored the match-winning goal in the stoppage-time against Hønefoss.
On 22 April 2013 it was reported that Berisha fractured his right elbow and will be absent for two months.
Berisha played for one match for Norway U15 in 2009, and the next year he played nine matches for Norway U16 where he scored three goals. In 2011 Berisha again scored three goals in nine matches while representing his country, this time for the Under-17 team. Berisha has also played eight matches for Norway U18, scoring three goals.
Like his brother Valon, he was approached by Kosovo when they became FIFA members in February 2016. However, unlike his brother who elected to represent Kosovo, he decided to keep representing Norway.As of 31 August 2017
Scores and results list Norway's goal tally first.