In March 2007 Alexandria was participating in the joint U.S. Navy/Royal Navy Ice Exercise 2007 (ICEX-2007), conducted in the Arctic Ocean with the Trafalgar-class submarine HMS Tireless (S88).

The exercise took place on and under a drifting ice floe, about 180 nmi (330 km; 210 mi) off the north coast of Alaska.

On 21 March 2007, Tireless experienced an explosion of a self-contained oxygen generation candle, she suffered only superficial damage, but two crew members were killed and one injured.

[12] On 19 August 2016, Navy machinist mate Kristian Saucier, 29, was sentenced by a U.S. District Court judge in Bridgeport, Connecticut, to one year in prison plus six months house arrest for taking and possessing six cell phone photos of Alexandria's classified propulsion system while working in her engine room in 2009.

The ship was also used as a filming location for the JAG and NCIS TV series, although she was referred to there as the fictional USS Cathedral City.