After only one season with the OHL’s Kitchener Rangers, David Shaw was selected by the Quebec Nordiques 13th overall in the 1982 Entry Draft. He spent his second season with the Rangers amassing 74 points in 57 games and was called up to the Nordiques for a brief two-game stint. The 1983-84 season saw much the same thing happen. Shaw had an exceptional year and was named an OHL first all-star team and Memorial Cup all-star team member. He was also called up to the NHL. After another season in the minors, this time with the AHL’s Fredericton Express, and another brief stop in Quebec, Shaw became a full time player in the NHL for the 1985-86 season.
Shaw played two full seasons with the Nordiques before being traded to the New York Rangers in 1987. His first season as a Ranger, 1987-88, saw him collect a career high in assists and points with 25 and 32, respectively. Shaw was in New York for just over three more seasons when he was traded to the Edmonton Oilers in 1991, and then two months later he was sent to the Minnesota North Stars. In the off-season, he was dealt yet again, this time to the Boston Bruins, where he saw a resurgence in his point production for the 1992-93 season, collecting 24 points in 77 games.
The Bruins dealt Shaw to the Tampa Bay Lightning after three seasons of service in Boston. He played three seasons for the Lightning, while spending some time with the IHL’s Las Vegas Thunder. Shaw was dealt one more time, going to the San Jose Sharks in 1998 and played for the Chicago Wolves of the IHL in the 2000-01 season.