Palat signed a five-year, $30 million contract with the New Jersey Devils on July 14, 2022. The two-time Stanley Cup winner with the Tampa Bay Lightning (2020, 2021) scored the game-winning goal in Games 3 and 5 of the 2022 Eastern Conference Final against the New York Rangers and Game 5 of the Stanley Cup Final. He has 12 game-winning goals in the NHL playoffs, third among active players behind Joe Pavelski of the Dallas Stars (14) and Evgeni Malkin of the Pittsburgh Penguins (13).

He was traded to the New York Islanders on Jan. 27, 2026.

Palat, a Czechia native, was one of the keys to the Lightning's run to the Stanley Cup in 2020. After not scoring a goal during Tampa Bay's first nine postseason games, Palat scored 11 in the final 16 -- including three during the Lightning's six-game victory against the Dallas Stars in the Stanley Cup Final. He was also second to teammate Nikita Kucherov in the playoffs with a plus-15 rating. He was named to Team Czechia's roster for the Olympic Winter Games Milano Cortina 2026.

The Lightning selected Palat in the seventh round (No. 208) of the 2011 NHL Draft but were not sure where the forward, who had gone undrafted the previous year, would fit into the organization. At the draft table there was some question about whether Tampa Bay should pick Palat or invite him to training camp.

As it turned out, the Lightning made a wise choice in using their final pick on Palat, who turned into a cornerstone player.

Palat impressed quickly with his two-way game at the start of the 2013-14 season. He finished second in voting for the Calder Trophy as the NHL's top rookie (linemate Tyler Johnson was also a finalist) after finishing plus-32 and scoring 23 goals, tied with Steven Stamkos for second-most as a rookie in Lightning history.

That performance helped Palat make the Czech Republic roster for the 2014 Sochi Olympics.

During the 2014-15 season, his second in the NHL, Palat (16 goals, 63 points in 75 games) helped form the most productive line in the League, skating alongside Kucherov and Johnson. The line, dubbed "The Triplets," combined for 200 points during the regular season. The line added 61 points in the Stanley Cup Playoffs, helping Tampa Bay reach the Cup Final for the second time in its history before losing to the Chicago Blackhawks in six games.

Palat settled into a role as a middle-six forward with one of the NHL's best teams. He scored at least 16 goals in three of the next five seasons and was a plus-player in all five, including plus-25 in 2019-20.