How do I write a letter informing someone they need to let an employee go?

[Freedom]

There is a person who works for a well known reputable institution who has been abusing their position. I do not work for this institution but have been a victim of their unprofessional conduct which brought about unwarranted consequences. I know of a few incidences of gossiping about this person's employers and colleagues and also giving out personal, private information that should not be public knowledge. I want to let the employer know of the unprofessional conduct from this person but am not sure how to go about doing so. I feel that this person is not a good fit for the institution. This person has worked for the institution for over 20 years but has had various superiors. The newest chief officer has been in place for over a year. I was recently told that this person's job is in question, but to what extent, I do not know. How should I go about addressing my concerns to the new person-in-charge?