Returning to Newport early in March 1951, Norris overhauled at Boston and trained in the North Atlantic and Caribbean until sailing on 19 April 1952 for her deferred first Mediterranean deployment.

Peacekeeping duty with the United States Sixth Fleet continued until 27 June, when she returned to Newport to prepare for "Operation Main Brace", a major NATO exercise in the North Sea that took place from 26 August to 12 October.

With Destroyer Squadron 24 she made an extended training cruise to South America from early January to late March 1957, visiting ports in Brazil, Argentina, and Uruguay between antisubmarine exercises with various Latin American navies.

Deployed again to the Mediterranean from 1 October 1964 to 18 January 1965 and 19 August–7 December 1965, Norris served in Polaris support operations as a missile tracking ship from 1 to 15 April 1966, and in the primary recovery force for Gemini X from 12 to 23 July.

Intensified operations in Vietnam called her with other ships of Destroyer Squadron 20 and they left Newport on 4 October for Panama and Yokosuka, arriving on 10 November.

As they had in Korea, her guns supported troops ashore, first driving back Viet Cong attempting to overrun Vũng Tàu on 21 November.

After four months on the gunline giving major service in the struggle to keep South Vietnam free, Norris completed a circumnavigation by returning via Suez to Newport, arriving on 25 April 1967.

After 20 years of service with Turkish Navy, Kocatepe (ex-USS Norris DD859) was decommissioned and sold as scrap to Hurdasan Anonim Sirketi in June 1994.