Wikipedia
A king-emperor, the female equivalent being queen-empress, is a sovereign ruler who is simultaneously a king of one territory and emperor of another. This title usually results from a merger of a royal and imperial crown (as in Austria-Hungary), but recognises that the two territories are different politically or culturally and in status (emperor being a higher rank than king). It also denotes a king's imperial status through the acquisition of an empire or vice versa.
The dual title signifies a sovereign's dual role, but may also be created to improve a ruler's prestige. Both cases, however, show that the merging of rule was not simply a case of annexation where one state is swallowed by another, but rather of unification and almost equal status, though in the case of the British monarchy the suggestion that an emperor is higher in rank than a king was avoided by creating the title "king-emperor" ("queen-empress") instead of "emperor-king" ("empress-queen").
Usage examples of "king-emperor".
Ethlinn and Maeve had said that Roxburgh could be trusted, but it would be better to see the King-Emperor himself.
As Roxburgh and I now stand at the left and right shoulders of the King-Emperor, so, in macabre travesty, Huon the Hunter and the Each Uisge, the most malign of all waterhorses, once long ago flanked their leader.
Despite herself she constantly pictured him as he might appear on the fields of conflict, if he lived: James the Sixteenth, King-Emperor, mounted on his armored warhorse Hrimscathr, the sword Arcturus scabbarded at his side and its damasked quillons catching the sun's rays.
He is the King-Emperor, whose very birth was witnessed by the Lord High Chancellor, not to mention a multitude of midwives and carlins.
Like the tail of a comet, a glittering train forever attended the King-Emperor.