Upon concluding the 2013–14 season, Stephenson signed a three-year entry-level contract with the Capitals and was immediately assigned to American Hockey League (AHL) affiliate, the Hershey Bears, on an amateur try-out.

Stephenson started his professional career with the Bears and played two full seasons with the team before making his NHL debut on October 15, 2015.

[8] His productive play as a rookie and sophomore earned Stephenson high preseason rankings from various scouting services.

[10] He also helped the Pats qualify for the WHL Playoffs for the first time in four years, where he recorded one goal and three assists in five post-season games.

[11] As such, he earned a final NHL Central Scouting Bureau ranking of 33rd amongst Canadian Hockey League (CHL) players.

[16] During his time at camp, head coach Barry Trotz placed him on a second line alongside Nathan Walker and Kevin Elgestål.

[21] As a result of his limited recalls, Stephenson finished the regular season with a new career-high 38 points through 72 regular-season AHL games.

Following his second career-best season, Stephenson signed a two-year, $1.3 million contract to remain with the Capitals organization on June 29, 2017.

[23] Although Stephenson was originally returned to the Hershey Bears to begin the 2017–18 season, he was recalled on October 24, 2017, after playing six games.

[24] As a result of numerous injuries to the Capitals lineup, Stephenson played on their top line during a 6–2 loss to the Vancouver Canucks on October 26.

[25] As a result of his performance, Stephenson was placed on a line with Lars Eller and Tom Wilson at the end of October which produced five goals and 13 points through six games.

[27] Throughout the season, Stephenson became a mainstay in the Capitals' bottom-six forward group and spent time on the penalty kill and in 3-on-3 overtime.

[31] As a member of the top line, Stephenson helped the Capitals qualify for the Eastern Conference final for the first time in 20 years.

[32] The Capitals met the Tampa Bay Lightning in the conference finals, where Stephenson assisted on a goal that helped Washington tie the series.

[34] Due to the suspensions of Tom Wilson and Evgeny Kuznetsov, Stephenson earned a spot on the top lines to begin the 2018–19 season.

[37] Throughout the season, head coach Todd Reirden consistently shuffled the fourth line and Stephenson often played alongside new teammates.

[34] On December 2, 2019, having contributed with just four points through 24 games, Stephenson was traded by the Capitals to the Vegas Golden Knights in exchange for a fifth-round pick in the 2021 NHL Entry Draft.

He made his debut the following day playing alongside Tomáš Nosek and Ryan Reaves, where he scored the opening goal in a 4–3 victory over the New Jersey Devils.

[47] As the Golden Knights qualified for the 2021 Stanley Cup playoffs, Stephenson missed three games against the Montreal Canadiens with an undisclosed injury.

[52] Stephenson became the third player of the expansion era to win a Cup with a team he had previously defeated for it, joining Scott Niedermayer (with New Jersey in 2003 and Anaheim in 2007) and Billy Carroll (with the New York Islanders in 1983 and Edmonton in 1985).