Heiskanen has justified the Dallas Stars taking the defenseman with the No. 3 pick at the 2017 NHL Draft. He was a key to the Stars' run to the Stanley Cup Final in 2020 with 26 points (six goals, 20 assists), the most by a defenseman in the postseason since Brian Leetch of the New York Rangers had 34 in 1994. His two assists in a 5-2 win against the St. Louis Blues on April 12, 2023 gave him 73 points to pass Sergei Zubov (71) for most in a season at the position in Dallas/Minnesota North Stars history, and 62 assists to pass Craig Hartsburg (60 in 1981-82) for most assists by a defenseman in a season in Stars history.

Heiskanen (493 games) became the third-fastest defenseman born in Finland (Reijo Ruotsalainen, 368 GP; Risto Siltanen (463) to reach 300 points in the NHL with an assist in a 7-0 win at the Montreal Canadiens on Nov. 13, 2025. It also moved him past Brad Maxwell for the fifth-most by a defenseman in Stars/North Stars history. Before the season, Heiskanen was among six players named to Team Finland's preliminary roster for the Olympic Winter Games Milano Cortina 2026, where he won a bronze medal after leading Finland defensemen with five points (two goals, three assists) in six games.

The native of Espoo, Finland, signed an eight-year, $67.6 million contract with the Stars on July 17, 2021, an average annual value of $8.45 million. He entered the NHL to start the 2018-19 season and quickly showed why the Stars had valued him so highly. He played all 82 games, finishing fifth on the Stars with 33 points (12 goals, 21 assists) and fourth with four game-winning goals. He scored his first NHL goal Oct. 25, 2018, against the Anaheim Ducks; at 19 years, 99 days, he was the second-youngest defenseman to score in Stars/North Stars history (Ron Meighan, 18 years, 207 days).

In the 2023 Western Conference First Round, Heiskanen became the fourth defenseman in NHL history with 30 assists in the Stanley Cup Playoffs at age 23 or younger, joining Paul Coffey (50), Cale Makar (45) and Ray Bourque (32). He required the third-fewest games (52) to reach the mark with the Stars/North Stars, behind forwards Bobby Smith (33 GP) and Brad Maxwell (44 GP).

Also that season, Heiskanen became the second rookie in franchise history to be selected to the NHL All-Star Game (Danny O'Shea, 1968-69). He also had a goal and an assist against the Nashville Predators in Game 1 of the first round, becoming the youngest defenseman in franchise history to score in the postseason (19 years, 266 days).

Heiskanen also made history prior to reaching the NHL. In 2017-18, he won the Pekka Rautakallio Award as the best defenseman in Liiga, the top professional league in Finland. At 18, he was the youngest player to win the award, finishing with 23 points (11 goals, 12 assists) in 30 games for HIFK.

During that season, Heiskanen also represented Finland at the 2018 IIHF World Junior Championship and the 2018 PyeongChang Olympics.