Prow played college hockey at St. Cloud State from 2012–2016. In his second game with the St. Cloud Huskies, Prow recorded two goals and an assist in a 8–3 win over the University of Alabama in Huntsville Chargers on October 19, 2012. In his sophomore season, Prow recorded a new career high of four goals and 19 assists, which he again tied in his junior year, and was named to the All-NCHC Academic Team. In 2015–16, Prow was named the captain of the Huskies and he guided them to their first NCHC Frozen Faceoff championship while tying the school record in wins. As a result, he was named a finalist for the Hobey Baker Award, marking him as one of the ten best players in men's college hockey; he was also named All-NCHC First Team and won the NCHC's Player of the Year, Defenseman of the Year, and Offensive Defenseman of the Year awards. He was also named a First All-American Team. Prow signed a two-year entry-level contract with the Pittsburgh Penguins on March 29, 2016. He joined the Penguins American Hockey League affiliate, the Wilkes-Barre/Scranton Penguins, as an amateur tryout to complete their season. He made his AHL debut on April 8, 2016, against the Lehigh Valley Phantoms.
Professional
On October 20, 2016, Prow was reassigned to the Penguins ECHL affiliate, the Wheeling Nailers, and he made his ECHL debut that night. He recorded two assists in the 4–3 loss to the Reading Royals. On October 22, Prow was promoted back to the AHL. He recorded his first AHL points that season, two assists, in a 6–1 win over the Syracuse Crunch after his promotion. On February 3, Prow recorded his first, and only, goal in a 5–2 loss to the St. John's IceCaps. Prow finished the season with the WBS Penguins and ended his rookie campaign with 16 points in 59 games. After attending the Pittsburgh Penguins 2017–18 training camp, Prow was reassigned to the WBS Penguins for the 2017–18 season. However, he was reassigned to the Nailers again on December 6, 2017. Prow played three games for the Nailers before returning to the WBS Penguins for the rest of the season. Prow completed his sophomore season with 17 points in 40 games. Prow re-signed a one-year contract with the Penguins on July 17, 2018. After participating in the Penguins 2018 Training camp, Prow was reassigned to the WBS Penguins. That season, Prow spiked offensively and was selected to participate in the AHL All-Star Classic after recording new career highs with 22 points in 32 games. His 10 goals at the end of December marked the first time a Wilkes-Barre/Scranton Penguin defensemen recorded double digits in goals by December 31 since the 2002–03 season. Prow left the Penguins at the conclusion of his contract to sign a two-year, two-way contract as a free agent with the Florida Panthers on July 1, 2019.
