[1] In the following 2010–11 season, with a relegated Rögle returning to the HockeyAllsvenskan, Everberg featured more prominently with the senior side, contributing with five goals and 12 points in 41 games.

Upon his eventual return in February, Everberg's developing power forward role became influential in promoting Rögle BK back to the Elitserien.

[3] After making a strong impression at the Avalanche's 2014 training camp with his size and skating ability, Everberg surprisingly made the roster to begin the 2014–15 season.

Towards the conclusion of the regular season, Everberg suffered a shoulder injury against the Nashville Predators on 7 April 2015, which required surgery with a 6-month recovery period.

[9] As an impending restricted free agent at season's end, Everberg opted not to sign with Colorado and return to Sweden in signing a two-year contract with Växjö Lakers of the SHL on 6 May 2016[10] In the opening game of the 2016–17 season, Everberg made an immediate impact in his return to the SHL, scoring the opening goal and adding another in a 5–2 victory over former club, Rögle BK, on 22 September 2016.

With the ambition to re-establish his NHL career, Everberg left the KHL as a free agent and agreed to a one-year, two-way contract with the Winnipeg Jets on 1 July 2018.

As a free agent in the off-season, Everberg opted to return to his roots, signing a five-year contract with original Swedish club, Rögle BK of the SHL, on 23 April 2019.

[18] Everberg, as a late bloomer, made his first appearance for Sweden at the international stage at the senior level of the Euro Hockey Tour during the 2016–17 season.

During the 2017–18 season, with the exclusion of NHL contracted players, Everberg was selected to represent Sweden at the 2018 Winter Olympics in Pyeongchang, South Korea.