Connolly is a big, skilled right wing with good offensive instincts who can play up and down the lineup. He showed his versatility during the 2018 Stanley Cup Playoffs, scoring nine points (six goals, three assists) in 24 games to help the Washington Capitals win their first Stanley Cup championship since entering the NHL in 1974. Two of the goals came during the Final against the Vegas Golden Knights and he had the primary assist on Lars Eller's Cup-winning goal with 7:37 left in the third period of Game 5 at T-Mobile Arena.
As a teenager, Connolly showed off his promise with his hometown team, Prince George in the Western Hockey League. At 16, he scored 30 goals and 60 points during his first full season in juniors to become the first WHL player since Patrick Marleau in 1995-96 to reach 30 goals at that age. Connolly was named the rookie of the year in the WHL and the Canadian Hockey League.