Following shakedown out of New London, Connecticut, the submarine underwent availability at her builder's yard from April to June 1966 before making a cruise to Faslane, Scotland, and the Caribbean Sea.

Following the completion of this yard period in December 1971, Tinosa resumed active operations off the eastern seaboard and into the familiar waters of the Caribbean Sea and continued the routine into the middle of 1972.

After operating out of Sardinia and Holy Loch during this period, she returned home in December to conduct tests in conjunction with a project sponsored by the Massachusetts Institute of Technology.

After a three-day visit to the United States Naval Academy in late April, where she served in a familiarization program for midshipmen, Tinosa underwent a tender availability alongside Fulton (AS-11) at New London.

In ensuing months, the submarine was twice deployed to Bermuda and operated off Andros Island before participating in joint United States-Canadian antisubmarine warfare exercises in December off the Florida coast.

After being dry-docked in auxiliary repair drydock USS Waterford (ARD-5) at New London from January to March 1974, Tinosa departed her home port on 19 May, bound for the Mediterranean, and conducted her second deployment with the Sixth Fleet through the summer months.