Shesterkin made his professional and KHL debut midway through the following 2013–14 season, recalled from MHK to close out the final 8 minutes for Spartak in relief of Alexei Ivanov in a 5–3 defeat to HC Ugra on 20 January 2014.

[2] In his eighth appearance, Shesterkin collected his first win, making 33 saves in a 3–0 shutout victory over HC Slovan Bratislava on 2 March.

[4] As the fifth-ranked goaltender entering the 2014 NHL Entry Draft, Shesterkin was selected in the fourth round, 118th overall, by the New York Rangers on 28 June.

[6] Shesterkin played in his first NHL preseason game on 21 September, stopping 36 of 40 shots in a 4–1 loss to the Philadelphia Flyers.

[8][9] On 6 January 2020, the Rangers recalled Shesterkin after having success for the Wolf Pack with whom he posted a 15–4–3 record and was named to the 2020 AHL All-Star Classic.

This attracted considerable speculation as to whether he should be a contender for the Hart Memorial Trophy as the league's most valuable player, seldom awarded to netminders.

[26][27] The Rangers finished second in the Metropolitan Division, and in the opening round of the 2022 Stanley Cup playoffs faced the Pittsburgh Penguins, whose starting goaltender Tristan Jarry was sidelined by injury.

[36] The Rangers advanced to the Eastern Conference Final for the first time since 2015, facing the two-time consecutive and defending Stanley Cup champion Tampa Bay Lightning.

[44] During a victory against the Carolina Hurricanes, Shesterkin suffered a "minor soreness" injury and missed a few games as a precaution, but returned against the New Jersey Devils.

[45] Earning an All-Star nod for the second consecutive season, Shesterkin became the sixth Rangers goaltender in franchise history to accomplish this milestone.

He joins Henrik Lundqvist, Gilles Villemure, Eddie Giacomin, Gump Worsley, and Chuck Rayner.