The contract to build Trepang was awarded to the Electric Boat Division of General Dynamics Corporation in Groton, Connecticut, on 15 July 1966 and her keel was laid down there on 28 October 1967.

Following her return to New London on 5 February 1972, Trepang underwent a routine post-deployment standdown and upkeep, as well as attack submarine training and equipment grooming in local operating areas.

She conducted a second extended deployment into the North Atlantic from 24 July to 25 September 1972, returning to New London via Halifax, Nova Scotia, Canada.

An interim four-week drydocking period at the Portsmouth Naval Shipyard at Kittery, Maine, preceded Trepang's 1973 operations before she headed south for weapons tests off the Florida coast.

She participated in several special operations with the Sixth Fleet during the increased tension brought on by the Yom Kippur War in the Middle East in October 1973.

Following sea trials in late October 1975, Trepang returned to New London, which once again became her home port, on 7 November for an intensive post-overhaul upkeep alongside submarine tender USS Fulton (AS-11).

The FBI discovered the plot when Edward J. Mendenhall and James W. Cosgrove, two of the accused conspirators, contacted an undercover agent seeking funds for training and supplies.

After four months in the Arctic, the "Trepang" sailed to HMNB Portsmouth before returning to its homeport, Naval Submarine Base New London, in Groton, Connecticut.

After a change of command in November 1988, "Trepang" deployed on a two-month unsupported ASW mission to the North Atlantic for which she was awarded a Meritorious Unit Commendation.

After completion of Pre-Overhaul Testing (POT), in March 1989 Trepang entered her first regular refueling overhaul at Portsmouth Naval Shipyard in Kittery, ME.

During the remainder of her career, Trepang conducted many "fast-attack submarine" drill missions as well as a Mediterranean cruise interrupted by a stay of many weeks in La Maddalena, Italy, and Haifa, Israel.

Her scrapping via the Nuclear-Powered Ship and Submarine Recycling Program at Puget Sound Naval Shipyard in Bremerton was completed on 7 April 2000.

[3] Components of 'Trepang', including mess tables, crew bunks, and engineering, were used in the "Fast Attacks and Boomers: Submarines in the Cold War" exhibit at the Smithsonian Museum of American History from 2000 to 2003.