Glory was the name of a Constitution-class starship that had come into the possession of a privateer named Diego DeBlazio. Glory is the name DeBlazio gave the vessel upon taking possession of the ship, it is not known what the vessel's original name was. (TNG novel: Blaze of Glory)
At one time, the ship was part of the United Federation of Planets Starfleet. Eventually the ship was decommissioned. At the time, the Federation often sold decommissioned ships to private entities. Such vessels were stripped of their armaments and engines prior to being sold, and once sold were refitted as impulse powered merchant vessels. The Glory was one such vessel disposed of in this manner.
The ship eventually made its way into Romulan hands. The Romulans refitted the ship - which included the installation of a cloaking device, and gave it to Diego DeBlazio so that the man could act as a cat's paw against Federation shipping. DeBlazio attacked a number of freighters, and even disabled a Starfleet cruiser.
DeBlazio's actions drew the attention of the USS Enterprise-D to the area. In an initial engagement, the Glory was able to stage a surprise attack on the Enterprise, but the Glory was no match for the Enterprise.
Eventually, DeBlazio figured out that the Romulans were going to betray him, and turned against them. The Glory assisted Jean-Luc Picard in battle against the Romulans, destroying a Romulan warbird in the process. He then headed for Romulan space, intending to harass their shipping network. (TNG novel: Blaze of Glory)