A jaded cop refers to a police officer who has become cynical and distrustful due to prolonged exposure to the darker side of life. If you want to avoid using this term, there are several synonyms to choose from. For example, you could use the term disillusioned cop, who has lost their faith in people or authority, or perhaps a world-weary cop who has seen too much of the dark side of life. Other synonyms include a tired cop who has exhausted his/her patience, weary cop who has lost enthusiasm for the job, or a blase cop who is no longer excited by the nature of their work.