Shortly after the establishment of the Dominion elements of the fleet traveled to Char due to Sarah Kerrigan's psionic emanations. The fleet was led by General Edmund Duke and contained elements of Alpha Squadron. It engaged zerg and protoss forces in orbit but was defeated. Many ships were either overrun by the zerg or destroyed by the Protoss Expeditionary Fleet that arrived shortly after. With the ground forces suffering disaster as well the fleet fell back from Char, and later another fleet was defeated by the protoss.
In the years following the Brood War, credits that might have been better spent on expanding the Fleet were instead spent by Arcturus Mengsk in his hunt for Jim Raynor. Even so, by the time the Second Great War broke out the fleet had been rebuilt to the point to be again a sizeable military force.
During the fighting, Prince Valerian Mengsk had the anti-Dominion Raynor's Raiders retrieving the components to a xel'naga device; Mengsk believed the device could deinfest Kerrigan and strike a decisive blow against the zerg. Once all the components were in hand, the prince took half the fleet, without formally informing Emperor Arcturus Mengsk, to attack Char. The battle group was accompanied by Raynor's Raiders, and overall operational command was given to General Horace Warfield. The fleet was heavily engaged but eventually fought its way from high orbit and into the atmosphere.
↑Duke: "Protoss Commander, this is General Edmund Duke of the Terran Dominion Armada. You are in violation of our air-space and have endangered human lives in your reckless attack against the Zerg. I order you to withdraw your ships immediately. If you fail to comply, I will not hesitate to open fire upon your vessels." Tassadar: "General Duke, I am Tassadar, and you are well known to me. Whatever leniency I extended to you and your comrades before, may have been in error. If you persist in halting our course, we will burn your pathetic fleet down to the last man." Duke: "I'm going to have to assume that was a hostile response..." StarCraft. Vivendi Games. Mission: Choosing Sides (in English). 1998.