(coexisting on another dimensional plane)
The ISS Shenzhou was almost identical in configuration to the USS Shenzhou of the prime universe, bearing the same registry (NCC-1227) and class. However, the ISS Shenzhou had several details that its counterpart lacked, such as the dagger emblem of the Empire adorning the dorsal side of the saucer and in the interior of the ship, armed guards, and agony booths to keep the crew in line. The lateral vector transporters were also updated with newer models.
In 2256, the vessel was under the command of Captain Michael Burnham. While in command, Burnham was ordered to hunt down Gabriel Lorca, who was attempting a coup against the emperor. Her shuttlecraft was destroyed during this operation and she was presumed dead. Captain Danby Connor then assumed command in her absence.
The following year, the Burnham of the prime universe posed as her counterpart, acting as though she had faked her death in order to capture Lorca. With her apparent Gabriel Lorca posing as the Imperial Starfleet Lorca, she returned to the Shenzhou and retook command from Captain Connor as part of a ruse to obtain intelligence that could help return the crew of the USS Discovery to their own reality. After she killed Connor in self-defense, the crew of the Shenzhou fell in line behind Burnham. (DIS: "Despite Yourself")
With Burnham in command, the Shenzhou carried out normal operations, periodically executing "traitorous" crew members by beaming them into open space. Captain Maddox ordered Shenzhou to the planet Harlak in order to destroy an insurgent camp and kill the alien rebel leader known as the Fire Wolf. When Burnham failed to use Shenzhou's torpedoes to destroy the camp outright, Emperor Georgiou bombarded the planet from orbit aboard her own vessel, the ISS Charon. Georgiou then ordered Burnham and Lorca to depart the Shenzhou aboard one of the ship's SHNZ 03 and rendezvous with the Charon. (DIS: "The Wolf Inside", "Vaulting Ambition")
The sets of the ISS Shenzhou were the same sets used for the USS Shenzhou and USS Discovery of the prime universe. The "upgrade" of the lateral vector transporter reflected changes made to the Shenzhou transporter room set for its use as the same room aboard Discovery, including the replacement of the single, circular transporter console (seen in "Battle at the Binary Stars") with two consoles to the left and right of the transporter pad seen throughout the rest of the series.
According to a fact sheet shown at a Mirror Universe exhibition running concurrent with San Diego Comic Con 2018, the ISS Shenzhou had a crew of 150 and a maximum speed of Warp 6. Unlike its counterpart, it was constructed at Tranquility Base, "Earth Moon".