Starfleet, also known as the Imperial Starfleet, was the Terran Empire's military organization in the mirror universe. Through Starfleet, the Empire conquered other planets and enforced its rule over those worlds (TOS: "Mirror, Mirror"). Spock later disarmed Starfleet, leaving the Empire vulnerable to the Klingon-Cardassian Alliance (DS9: "Crossover").
In Star Trek: Mirror Wars, the second Terran Empire returned to power and created a new Starfleet. It is unknown if it was called "Starfleet" but the ships were exactly like ships from the primary universe.
In Star Trek: Shattered Universe, the Imperial Starfleet was rekindled in the early 2380s until at least 2383, after the Alliance had barely made a move against the Terran Rebellion. During this time, a shipyard was established to create Terran-style starships. Although this new Starfleet was growing with hopes to match the Alliance, its internal politics and reawakening greed began to lead it toward a downward spiral.
In Taskforce Equinox, the Terran Rebellion as of 2379, having a need to shift away from their dependence on Raiders, moved to larger more Terran style warships (based on designs stolen from the Prime Federation) however, lacking the proper skill in operating such large vessels the Rebellion relied heavily on former Imperial officers to operate them who quickly resurrected a lot of Imperial protocol's including the name. ISS VanguardTaskforce Equinox