Clay was drafted in the eighth round (221st overall) of the 1992 NFL draft by the Detroit Lions. He played for the Lions until 1995, after which he spent three seasons with the New England Patriots, and his final season with the New Orleans Saints. During his time with the Patriots, he earned the nickname "Big Play" for his interception during the Patriots victory over the Jacksonville Jaguars in the AFC Championship that sent the Patriots to the second Super Bowl in franchise history.
Clay is the nephew of Dwight Clay who was a basketball player for the University of Notre Dame. Dwight Clay was nicknamed "The Iceman" and is famous for hitting the game winning jump shot that ended UCLA's NCAA all-time record 88-game winning streak on January 19, 1974.