From June 1994 to July 2008, he held the chair for constitutional, international, and European law at the University of Potsdam.
After graduating from high school in Karlsruhe in 1962, and then completing military service, Klein studied law in Freiburg im Breisgau, Göttingen, Lausanne, and Heidelberg from 1964 to 1968.
From 1974 to 1976, Klein was seconded to the Federal Constitutional Court as a research assistant and reported to the then President Ernst Benda.
From 1995 to 2002, Klein was a member of the United Nations Human Rights Committee in New York and Geneva.
In September 2019, he was one of around 100 constitutional law teachers who came out with the open call for the right to vote Reduce the Bundestag!