The Terran emperor or empress, sometimes also referred to as caesar, was the emperor of the Terran Empire, a repressive interstellar government dominated by the Terrans from Earth in the mirror universe.
In January 2155, Jonathan Archer intended to become emperor. However, Hoshi Sato declared herself empress of the Terran Empire after seizing control of the USS Defiant and ordering Starfleet's unconditional surrender. (ENT: "In a Mirror, Darkly, Part II")
In the 2250s, Philippa Georgiou was the Terran emperor. (DIS: "The Wolf Inside")
Upon reading data files obtained by rebels fighting the Empire, Michael Burnham referred to the emperor as "faceless". (DIS: "Despite Yourself")
In 2267, Marlena Moreau suggested that Captain Kirk might aspire to become caesar. (TOS: "Mirror, Mirror")