An undrafted player, Šustr made his NHL debut with the Lightning in 2013 after playing three seasons of college ice hockey with the University of Nebraska Omaha.

Šustr grew up in the city of Plzeň, but after finding little opportunity in his home town, was encouraged to move to the United States at the age of 17 to play junior hockey.

[6] He played eight regular season games with Syracuse, scoring two goals and adding an assist,[3] while the Crunch reached the Calder Cup Final against the Grand Rapids Griffins.

[9] On 30 March, the Lightning announced that Šustr would be out one-to-two weeks with an upper body injury, but was expected to return in time for the start of the 2015 playoffs.

[12] On 25 October 2016, Šustr skated in his 200th career NHL game, which came in a 7–3 Lightning victory over the Toronto Maple Leafs at the Air Canada Centre.

[14] After six seasons within the Lightning organization following the 2017–18, Šustr left as a free agent and agreed to a one-year, $1.3 million contract with the Anaheim Ducks on 5 July 2018.

However he was limited to just 5 games over the duration of the year, reassigned for the majority of the campaign to add a veteran presence to AHL affiliate, the San Diego Gulls.

[21] At the conclusion of the season, as a pending free agent, Šustr was traded by the Ducks to the San Jose Sharks in exchange for Andrew Agozzino on 27 June 2023.

[22] While not offered a contract by the Sharks, Šustr left North America as a free agent and agreed to a one-year deal with German outfit, Kölner Haie of the DEL, on 10 July 2023.