private detective 
(also private investigator)
noun
A freelance detective who carries out covert investigations on behalf of private clients.Behind the scenes, private investigators are doing covert surveillance for government agencies and the insurance industry, or tracing people to serve court orders....
- We as a municipality then continued our investigation by appointing a private investigator.
- It remains unclear how much information the government has about his actions and whether the lawyers and clients who retained the private investigator knew of any wiretapping.
Synonyms
private investigator, detective, operative;
British enquiry agent
informal private eye, PI, sleuth, snoop
North American informal private dick, peeper, shamus, gumshoe
informal, dated hawkshaw, sherlock
North American dated Pinkerton