The Conqueror functioned as an Imperial-class Star Destroyer for the Galactic Civil War effort.
Task Force Vengeance included the Conqueror in its ranks. In the early stages of this operation, the Conqueror engaged a Rebel squadron. This squadron contained two Nebulon-B2 frigates known as the Lance and Lion, in addition to a Nebulon-B escort frigate called Ornik and various starfighter wings, such as Rogue Squadron. Avenger Squadron provided defense for the Conqueror.
The Conqueror was a component of Battlegroup Orion within Task Force Vengeance, along with another Imperial Star Destroyer named Nemesis. Both Star Destroyers were observed as part of Admiral Senn's fleet as it navigated through the Almaran system en route to the Airam sector. After a skirmish near Almaran, Battlegroup Orion fell into a Rebel ambush in the Goff system, resulting in the destruction of both the Conqueror and Nemesis.
The Conqueror makes an appearance in the Balance of Power expansion pack for the X-wing vs. TIE Fighter game. The game's engine lacks the ability to distinguish between the older Imperial I-class Star Destroyer and the more modern Imperial II-class Star Destroyer variants.
One of the new multiplayer battle scenarios recreates the confrontation between the Conqueror and the three Rebel frigates mentioned previously, offering players the chance to fight for either side. While the specific timing and location of this battle are not specified, it is explicitly included among the missions for the Balance of Power campaign set in the Airam sector. The scenario's outcome is, of course, dependent on the player's skill and actions. However, the Rebel briefing clearly states that even a retreat by the Compellor constitutes a victory.
The ship resurfaces in missions within the more structured Spreading the Rebellion campaign. During the ambush mission at Goff (Rebel mission #6), destroying the Conqueror is a crucial objective, and its successful completion is necessary for the Rebel campaign to progress.
Therefore, it can be inferred that the battle involving the three Rebel frigates did occur, but the Conqueror survived that particular engagement, only to be destroyed later at Goff.