Between 28 June and 18 October 1963, "Alexander Hamilton" carried out two shakedown cruises, one for each of her crews. Following those operations, she conducted post-shakedown availability. After trials early in 1964, she departed the United States East Coast on 16 March 1964 to deploy to Rota, Spain, her base of operations. She conducted deterrent patrols out of that port for the remainder of 1964 as a unit of Submarine Squadron 16. In January 1965, she transferred to Submarine Squadron 14 and was rebased at Holy Loch, Scotland. Her cycle of patrols from there lasted until 2 June 1967, at which time she returned to the United States at Charleston, South Carolina. Later that month, she moved north to New London, Connecticut, and from there into the Electric Boat shipyard on 18 June 1967 to begin her first overhaul and nuclear refueling.