Parker attended Duke University, where he received a B.A., magna cum laude, in political science and comparative area studies, in 1977.

[8][9] From 1983 to 1984, Parker served as a law clerk to the Honorable Amalya L. Kearse of the United States Court of Appeals for the Second Circuit.

[11] Parker became a partner in the corporate department at Cravath in June 1990, and focused his practice on commercial bank financing, as well as a broad range of other matters in the areas of general corporate practice, securities offerings, mergers and acquisitions, and derivative transactions.

[15] In March 2017, after what was described as a “successful turn as Cravath’s Presiding Partner” during which he made “principles and culture a focus of his tenure,” Parker left Cravath to become the General Counsel of Wells Fargo, then stating that he intended "to make the legal department of Wells Fargo a beacon for other departments in ethics.”[16][17] In March 2019, upon the retirement of Wells Fargo CEO and president, Timothy J. Sloan, Parker was elected by the board of directors to serve as the chief executive officer and president, on an interim basis, while the board conducted a search for a permanent CEO.

[19] Parker returned to the General Counsel role in October 2019, and left Wells Fargo in March 2020.