British South Africa Company's Police, a police force of British South Africa Company over time became the national police force of South Rhodesia (present-day Zimbabwe). This force was first to use Maxim machine guns against natives which led to about 5000 casualties from the native side (with nearly no casualties from the corporate side).
Going further in the past I think medieval Rome was a place that was policed by private forces of different clans at a time with some clans policing certain districts and some the others. A person could not visit the districts policed by an adversary clan.
It should be noted however that state-hired private police in theory should differ from a private police hired by a private person or company.
The main concern with privately-hired police force are as follows:
Such police force may protect only the private interests of those who pays while ignoring others
Such police force may ignore the laws in favor of those who hired them
Such police puts people in unequal position before the law so that those who can pay protected better
The main concerns with state-hired private police are as follows:
The police corporation may itself become immune against investigations and nontransparent due to corporate subordination
There is a room for corruption
The police may abandon their work once the state or municipality runs out of money or does not manage to pay in time
The police may want to investigate only those crimes that are good for statistics and as such, for the profits, and possibly, hide other crimes
Left-wing politicians may be concerned that private police may prosecute left-wing and workers' political movements in a case of political disputes or strikes because the victory of the left-wing political force is contrary to the interests of the firm and its owners.
A recent science-fiction film had been themed around police privatization, "Tokyo gore police". The police force of Tokyo has been privatized, the father of the main heroine, a police officer, was shot during an anti-privatization rally. The privatization led to the uncontrolled corruption of the management. The film also features fictional funny "advertisement reels" supposedly by the police corporation where they advertise the population on how well they can protect them.