On 1 July 1956, she was assigned to the newly established Destroyer Squadron 36 (DesRon 36), composed of destroyer escort types specially configured for anti-submarine missions and yet maintaining the capability to handle all destroyer missions. During the last week of November and the early part of December 1959, "Robert L. Wilson" and two other escort destroyers participated in Operation "Monsoon," manning sea-air rescue stations for the Presidential flight to Europe from the United States. She then operated in the western Atlantic and Caribbean until a Norfolk Navy Yard overhaul in the summer of 1960.