She was named for Chief Watertender Charles Kleinsmith (1904–1942), who was posthumously awarded the Navy Cross for his heroism during the Battle of Midway.

During the Battle of Midway on 4 June 1942, Chief Watertender Kleinsmith maintained auxiliary power on Yorktown after an intense Imperial Japanese Navy bombing attack extinguished the fires in all of her boilers but one.

Originally a Rudderow-class destroyer escort designated DE-718, Kleinsmith was re-designated as APD-134 on 17 July 1944, even before being laid down on 30 August 1944 at the Defoe Shipbuilding Company, Bay City, Michigan.

Departing on 4 August for the Pacific, the high-speed transport steamed via the Panama Canal, San Diego, and Pearl Harbor, and reached Buckner Bay, Okinawa, on 1 October.

She then sailed from Sasebo via the Marshall Islands and Pearl Harbor, arriving at San Francisco on 24 March with 118 returning veterans embarked.

She served primarily as an amphibious command ship; many of her cruises carried her into the Caribbean, where she operated out of Puerto Rico, the Virgin Islands, and Guantanamo Bay.

Arriving at Gibraltar on 15 March with UDT personnel embarked, she deployed with the 6th Fleet and participated in amphibious operations that ranged from Oran, Algeria, to Phaleron Bay, Greece.

After serving as an amphibious control ship, she departed Gibraltar on 26 June for the United States, arriving at Little Creek on 6 July.

In response to an urgent request from King Hussein of Jordan, whose government was threatened with leftist-oriented, Egyptian-supported subversion, Kleinsmith departed La Spezia, Italy, on 25 April for the Levantine Coast.

Arriving off Beirut, Lebanon, on 30 April, she joined ships of the 6th Fleet in a formidable display of seapower, designed to show U.S. determination that the integrity and independence of nations in the Middle East would be guaranteed against Communist subversion or aggression.

In the early 1970s, Tien Shan was fitted with a second 5-inch/38 mount aft, a Sea Chaparral surface-to-air missile launcher, and ASW torpedo tubes.