Rembert was a key member of the 1985 AFC champions who played the Chicago Bears in Super Bowl XX in New Orleans. He was also selected to the AFC Pro Bowl team twice (1988 and 1989).
As a key player for the 1985 AFC champions, Rembert participated in the game against the Chicago Bears during Super Bowl XX in New Orleans. Additionally, he was chosen to the AFC Pro Bowl team twice (in 1988 and 1989).