He has previously played for the Minnesota Wild, Vegas Golden Knights, Carolina Hurricanes, Florida Panthers, Nashville Predators and Boston Bruins.

[5] After leaving the USHL, Haula totaled 42 goals, 82 assists and 124 points in 114 games during three seasons of college ice hockey with the Gophers.

The Minnesota Wild made him a qualifying offer to retain his NHL rights and, on 27 July 2015, Haula filed for Salary Arbitration.

[10] The 2015–16 season saw a breakout year for Haula, as he set NHL personal bests in goals, assists, and points, more than doubling his previous highs in all three categories.

At the completion of his fourth season with the Wild in 2016–17, as a restricted free agent Haula was left exposed for the 2017 NHL Expansion Draft.

After agreeing to a three-year, $8.25 million deal with the Vegas Golden Knights, Haula was Minnesota's required selection for the draft on 21 June 2017.

[14] Upon returning to the Golden Knights, Haula was moved around the lineup and centered a line between David Perron and James Neal, resulting in an increased output.

[16] On 1 February, Haula scored a goal to help the Golden Knights set a record for most wins by an NHL team in its inaugural season.

[18] Following his career-high regular season, Haula and the Golden Knights faced off against the Los Angeles Kings in the first round of the 2018 Stanley Cup playoffs.

[26] While playing on this line, he sustained a right leg injury when he was hit by Toronto Maple Leafs forward Patrick Marleau and was expected to miss three games.

[28] On 26 June 2019, Haula was traded by the Golden Knights to the Carolina Hurricanes in exchange for prospect Nicolas Roy and a conditional fifth-round draft pick.

[34] As an impending free agent, Haula was dealt at the NHL trade deadline by the Hurricanes along with Lucas Wallmark, Eetu Luostarinen and Chase Priskie to the Florida Panthers in exchange for Vincent Trocheck on 24 February 2020.

[35] On 23 December 2020, approaching the delayed 2020–21 season, Haula signed as a free agent in agreeing a one-year, $1.75 million contract with the Nashville Predators.