The Julio-Claudians used German bodyguards, and the later Byzantine Emperors also used foreign bodyguards, in this case the Varangians. In the New Dynasty period of ancient Egypt, a tribe called the Medjay evolved from foreign mercenaries into paramilitary police who guarded areas of royal interest, like the Valley of Kings (I think, Egyptology is not my area of expertise). I wonder if there any other examples from history of regimes who specifically used foreign units to guard the King/Emperor or things of interest to him?
They were at least extensively used by the French kingdom (Gardes Suisses and Garde Écossaise, later the Mamluks of Napoleon). The modern Vatican Swiss Guard is another example. On the other hand, the Papal city of Rome before 1870 was protected by a French detachment, which is quite in the blur between “bodyguards of the head of state” and “foreign occupation forces”.