Alt was selected 53rd overall in the 2010 NHL Entry Draft by the Carolina Hurricanes. He joined the Golden Gophers of the Western Collegiate Hockey Association in the 2010–11 season. After missing the first game of the season, he participated in 35 consecutive games. His 10 points ranked fourth among Gophers defenders in points. He played in his first NCAA game on October 9, 2010 versus Massachusetts. In the same game, he logged his first career NCAA point, an assist on the game-winning goal. January 15, 2011, would mark the first NCAA goal of his career, as he scored versus divisional rival North Dakota. Alt participated in the 2010 U.S. National Junior Evaluation Camp in Lake Placid, New York. Focused on sharpening his defensive shutdown ability, Alt took on a leadership role as a sophomore in the 2011–12 season, while increasing his points totals with 5 goals and 22 points in 43 games. In his junior season in the 2012–13 season, Alt fully transitioned to a shutdown defense role in recording just 7 assists in 39 games for the Gophers. During the campaign, Alt's NHL rights were traded by the Hurricanes to the Philadelphia Flyers on January 13, 2013 along with Brian Boucher for Luke Pither. For a second consecutive year he was selected to the WCHA All-Academic Team with a 4.0 grade average.
Professional
Philadelphia Flyers
After his third season of collegiate hockey with the Golden Gophers having scored 39 points in 117 collegiate games, Alt signed a three-year entry level contract with the Philadelphia Flyers on April 7, 2013. He immediately joined the Flyers American Hockey League primary affiliate, the Adirondack Phantoms on an amateur try-out contract to finish the 2012–13 regular season. Appearing in 6 games with the Phantoms, Alt earned praise from veteran NHL and blueline partner in Andreas Lilja. In his first full professional season, Alt was reassigned to continue with the Adirondack Phantoms for the duration of the 2013–14 season. He tied second on the club amongst defenseman with 22 assists and 26 points in 75 games. In the 2014–15 season, Alt was again reassigned to the AHL by the Flyers, joining new affiliate, the Lehigh Valley Phantoms for their inaugural season. Limited to just 44 games through injury, Alt returned with 2 goals and 10 points. In continuing his upward development the Flyers, Alt was recalled on emergency, and made his NHL debut in playing 9:25 with Philadelphia in a 3-2 shootout defeat to the San Jose Sharks on March 28, 2015. In the final year of his entry-level contract, Alt remained exclusively in the AHL with the Phantoms in the 2015–16 season, appearing in a further 72 games, paired alongside Samuel Morin in a shutdown role, and while also collecting 4 goals and 19 points. On June 26, 2016, he agreed to a one-year, two-way contract to remain with the Flyers. He was familiarly reassigned to return for his fourth season in the AHL in 2016–17. He was limited to just 40 games through injury, recording 1 goals and 11 points as the Phantoms reached the post-season for the first time in franchise history. Despite his reduced impact he placed second on the club in plus-minus. As an impending restricted free agent, Alt was again re-signed to a one-year, two-way contract to return for his sixth season within the Flyers organization on June 27, 2017. In preparation for the 2017–18 season, Alt was among the last cuts at the Flyers training camp and was familiarly assigned to Lehigh Valley. As the Phantoms best defenseman to start the year, Alt returned to the NHL for the first time in three seasons, as he was again used on an emergency basis in a 4-3 overtime defeat to the Arizona Coyotes on October 31, 2017. He was later officially recalled and featured in 7 more games before he was returned to the Phantoms on December 30, 2017. Alt posted 10 points in 23 games in the AHL before receiving his third recall to Flyers on January 22, 2018.
Colorado Avalanche
As the Flyers reserve depth blueline, Alt was a frequent healthy scratch and failed to feature in a game in over a month before he was placed on waivers in order to return to the AHL. On February 26, 2018, Alt was claimed off waivers by the Colorado Avalanche. With the Avalanche vying for a playoff position, he assumed the same role with the club and remained in the press box until making his belated debut with Colorado in a 2-1 shootout victory over the Vegas Golden Knights on March 24, 2018. He featured in 7 scoreless games with the Avalanche to end the regular season and remained a healthy scratch in their first-round defeat to the Nashville Predators in the playoffs. On May 11, 2018, Alt gave up his impending free agent status in signing a two-year, two-way extension with the Avalanche. After attending his first training camp with the Avalanche, Alt was among the last cuts prior to the 2018–19 season. He was reassigned to new AHL affiliate, the Colorado Eagles, and was selected as team captain on October 4, 2018.
