Quarless played for Penn State's football team under legendary coach, Joe Paterno. Quarless had a breakout season as a true freshman in the 2006 season. Success in the 2007 season was limited due to suspensions and loss of his starting position at tight end. Quarless saw limited playing time in 2008 until the Illinois game when he started in the place of the injured starter and caught a key 4th quarter touchdown. He caught the game-winning catch in the 2010 East-West Shrine Game.
He was drafted by the Packers in the fifth round of the 2010 NFL Draft with the 154th overall selection. On July 12, 2010, Quarless signed with the Packers. He made the 2010 team as a back-up tight end, playing behind Jermichael Finley, Donald Lee, and Tom Crabtree.
After injuries to Finley and Lee, Quarless was inserted as the starting tight end. He made his first NFL career touchdown against the Minnesota Vikings (albeit, having his back touch out-of-bounds which would have been overturned if challenged). At the end of the 2010 regular season, he had 21 receptions for 238 yards, averaging 11.3 yards per catch.
During the 2011 season, he had three receptions for 36 yards and was the primary backup to Jermichael Finley. He suffered a season-ending knee injury in a 4th quarter kickoff return in the 38-35 win against the New York Giants on Sunday December 4, 2011. He was placed on injured reserve the following week. The injury was so significant that it may end his career as there is speculation that he may miss the entire 2012 season after surgery.