After the expiration of his term, Cooper took over the "Dean Acheson chair" at the prestigious Washington law firm of Covington & Burling. In 1972, he was chosen as the commencement speaker at Centre College, where he had served as a trustee since 1961. At the ceremony, he became the first recipient of the Isaac Shelby Award, named for two-time Kentucky governor Isaac Shelby, the chair of the college's first board of trustees. In 1973, Cooper resisted an attempt to name a federal building in his honor. Upon the completion of the dam that formed Laurel River Lake in 1977, Congress proposed naming the dam and lake after Cooper, but again, he declined. He was pleased, however, that the Somerset school system chose to name a program to teach and reinforce leadership skills the John Sherman Cooper Leadership Institute.