Following the war, Stump underwent flight training at Pensacola in 1919 and 1920, and he earned an M.S. in aeronautical engineering from the Massachusetts Institute of Technology in 1923. Stump then served in Torpedo Squadron 2 on the experimental aircraft carrier Langley. Later, he was navigator of the carrier Lexington and then executive officer of the carrier Enterprise in 1940 and 1941.
Stump's World War II service started with his transfer in January 1942 from commanding officer of the Langley to the staff of the commander-in-chief of the Asiatic Fleet. Following the dissolution of that command, he spent eight months as air officer to the commander, Western Sea Frontier. In December 1942, Stump commissioned the new carrier Lexington, and he commanded her in operations against Tarawa, Wake, the Gilbert Islands, and Kwajalein.
Stump commanded escort Carrier Division 24 for most of 1944. As part of Task Force (TF) 52, he supported landings in the Mariana Islands in the summer of 1944. Stump commanded Task Unit 77.4.2 (known as "Taffy 2") during the invasion of Leyte in the fall of 1944. During this operation, his escort carriers engaged Admiral Kurita Takeo's powerful Center Force at the battle off Samar and sank the Japanese heavy cruiser Chikuma.
Stump commanded Task Unit 77.12.1 in support of the landings at Mindoro in December 1944. He then commanded the San Fabian Carrier Group during the landings on Luzon in January 1945. In the spring of 1945, Stump supported the invasion of Okinawa with his escort carriers.
Stump became chief of Naval Air Technical Training in June 1945, a post he held until his promotion to vice admiral in December 1948. In July 1953, Stump became commander in chief, Pacific and Pacific Fleet. Later, in March 1955, he was appointed U.S. military adviser to the South East Asia Treaty Organization (SEATO). Stump retired in August 1958. He died at Bethesda, Maryland, on 13 June 1972.
Morison, Samuel E. History of United States Naval Operations in World War II. Vols. 2, 4, 5, 9, 10, and 11. Boston: Little, Brown, 1947–1952.; Reynolds, Clark G. Famous American Admirals. Annapolis, MD: Naval Institute Press, 2002.