Originally drafted by the Washington Senators, Pryor was picked in the 6th round of the 1971 amateur draft (130th overall) and was the last position player draft pick of the Senators to play in the major leagues. He debuted in the majors with the Senators' later incarnation, the Texas Rangers, in 1976. Pryor was a member of the World Series-winning Kansas City Royals in 1985.
Pryor now lives in Kansas City. In 1995, he founded Life Priority, a nutritional supplements company, in Lenexa, Kansas. In 2005, he formed Sports-Aholic, Inc. Greg is now a co-host on a baseball-themed radio show called "The Ballgame" in Kansas City on ESPN 1510 AM.