[2] At the completion of his second season with the Blades, Hájek was signed to a three-year, entry-level contract with the Tampa Bay Lightning on 21 March 2017.

[3] He immediately joined the primary affiliate, the Syracuse Crunch of the AHL on an amateur try-out to play out the remainder of the 2016–17 season.

On 26 February 2018, Hájek was traded to the New York Rangers, along with Vladislav Namestnikov, Brett Howden, and two draft picks, for Ryan McDonagh and J. T.

[4] Hájek recorded his first career NHL assist off a goal by Mika Zibanejad during the 2019–20 season opener against the Winnipeg Jets on 3 October.

[9] Hájek left the Rangers organization after five seasons and was later signed as a free agent to a professional tryout deal with the Pittsburgh Penguins on 30 August 2023.