The Patriots selected Sims as the first overall pick in the 1982 NFL Draft, making him only the third Longhorn to receive such an honor. He finished fourth in AFC Defensive Rookie of the Year voting that season, which included a trip to the playoffs for the Pats.
Over Sims' eight-season career with the Patriots, he played 74 games and recorded 17 sacks. His best season came in 1985 when he registered 5.5 sacks in 13 games, helping the Patriots reach Super Bowl XX. Unfortunately, a broken leg late in the season prevented Sims from playing in the championship game.
Sims' career was impacted by injuries which limited him to only one complete season in 1984. In 1987, he underwent back surgery, and in 1988, a ruptured Achilles tendon forced him to miss the entire season. Despite these setbacks, Sims returned in 1989, playing most of the season before a knee injury sidelined him for the final game.
That would be his final season in the NFL, completing an eight-year career, all spent with the Patriots, which included a conference championship.