After four years with the Sibir organization, Zaitsev joined his hometown CSKA Moscow, after which he began to attract international attention.

[2] During the subsequent season's playoffs, he led all defencemen in scoring with 13 points (tied with Sami Lepistö and Chris Lee), while helping the top-seeded CSKA to the Gagarin Cup finals, where the team lost in the deciding Game 7 to Metallurg Magnitogorsk.

[1] He made his pre-season debut with the club on 2 October, scoring a goal in a 3–2 win over the rival Montreal Canadiens.

On 12 October 2016, Zaitsev made his official NHL debut in a 5–4 loss to the Ottawa Senators in the 2016–17 season opener, and was singled out for his good play by coach Mike Babcock.

[6] In the playoffs, Zaitsev missed the first two games[7] and upon his return, was tasked with shutting down Alexander Ovechkin's line in the Maple Leafs' series with the Washington Capitals.

[13] He finished the 2018–19 season with 14 points in 81 games and faced criticism for his play during the playoffs in which he led the Maple Leafs in turnovers with 11.

[16] On 1 July 2019, Zaitsev was traded (along with Connor Brown and Michael Carcone) to the Ottawa Senators in exchange for Cody Ceci, Ben Harpur, Aaron Luchuk and a third-round pick in the 2020 NHL Entry Draft.

[28] On 4 July 2024, as an unrestricted free agent, Zaitsev returned to the KHL, signing a four-year contract with SKA St.