A free agent for the 2019–20 season, Tanev signed a contract with the Penguins, where his line with Teddy Blueger and Zach Aston-Reese was tasked with tiring out other teams' leading scorers.

The Seattle Kraken selected Tanev in the 2021 NHL Expansion Draft, and he played with the team for the first half of their inaugural season before suffering an anterior cruciate ligament injury.

[3] In lieu of playing ice hockey, Tanev filled his adolescence with cross country running, track and field, and soccer, and he practiced his skating independently with a private skills coach.

After experiencing a growth spurt during his final year at East York Collegiate Institute, Tanev was able to secure a roster spot with the Markham Waxers of the Ontario Junior Hockey League (OJHL).

[6] After spending the offseason playing in the Vancouver Canucks' prospect camp, Tanev joined the Surrey Eagles of the British Columbia Hockey League.

[8] Tanev made his collegiate debut on October 13, 2012, skating on the left wing of a line that also featured Noel Acciari and Chris Rooney for the Friars' 4–2 loss to Boston University.

[20] They defeated the Quinnipiac Bobcats in the first round of the NCAA tournament, with Tanev picking up an assist in the process,[13] before losing to the Union Dutchmen in the East Region finals.

[22] He played in his 100th collegiate hockey game on February 14, a 3–2 win over Notre Dame, becoming the 148th Friar in program history to reach the milestone and the fifth of the season.

[42] He struggled to produce outside of that night, with two goals and two assists through 35 games, and was sent down to the Manitoba Moose, the Jets' American Hockey League (AHL) affiliate, on December 28 to make room for players returning from the injured reserve.

[45] Ten days later, Tanev was recalled again as defenceman Tobias Enström was sidelined with a lower-body injury,[46] and both he and Julian Melchiori were returned to Manitoba on February 22, when the Jets were placed on a five-day break.

[55] Tanev posted a total of four goals and six points in 17 playoff games before the Jets were eliminated by the Vegas Golden Knights in the Western Conference finals.

[59][60] Playing on a fourth-line checking unit with Copp and Lowry,[61] Tanev received his first game ejection on October 22 after his hit on St. Louis Blues skater Ryan O'Reilly.

[62] Tanev built a reputation during the 2018–19 season for his willingness both to score and to block shots, such as on February 1, when he was hit near the head by a puck off the stick of Columbus Blue Jackets defenceman Zach Werenski.

[67] Tanev, who had one goal and one assist in five playoff games, revealed after their elimination that he had surgery to repair the finger that Staal broke before joining Winnipeg for the postseason.

[69] Tanev's primary line during the 2019–20 season, winging Teddy Blueger and Zach Aston-Reese, came about by accident after injuries required coach Mike Sullivan to shuffle his starting line-up.

As the season progressed, they were used primarily to exhaust opposing teams' top scorers, allowing players like Sidney Crosby and Jake Guentzel to focus on their own offensive production.

[72] When the NHL returned to play in July for the 2020 Stanley Cup playoffs, Tanev was one of 31 players invited to the Penguins' quarantine bubble in Toronto.

[73] The Penguins took an early postseason exit, losing to the Montreal Canadiens in a four-game opening-round series,[74] with Tanev allowing the turnover that led to the elimination goal.

[77] Both captain Sidney Crosby and team president Brian Burke defended Tanev, arguing that the hit was clean and Tinorid's injury accidental.

[90] While recovering from his injury, Tanev took on an outreach role with the team which included him participating at youth hockey clinics and holding a virtual meeting with season-ticket holders.

[91] Following the conclusion of the 2023–24 NHL season, Tanev accepted an invitation to make his international debut for Canada with the senior national team at the 2024 IIHF World Championship.

[102][103] The stunned expression on Tanev's face on his official team head shot with the Pittsburgh Penguins, which he attributed to having seen a ghost when his picture was taken, became an Internet meme in 2020.