Have a system for managing conflicts. Have open conversations about real topics. Encourage people to broadcast their own messages. Take responsibility if you're guilty, or defend yourself if not, when you confront your colleagues or boss over gossip or inappropriate behavior.
You must acknowledge your participation in any unsolicited gossip or discussion and assure your boss that this attitude will not continue. However, do not allow false accusations to be made if they are not justified and defend yourself against them so that your employer doesn't penalize you for fallacious accusations. Protect yourself by avoiding conflict situations, so that your abilities are not overshadowed by your participation in dramatic situations in the workplace. If setting limits doesn't work, tell the person looking for theater that they have a project to finish or a meeting to attend.
Managing gossip appropriately will help you establish yourself as a leader and foster a positive work environment that increases retention and instills a sense of psychological safety. Proactively creating a culture that doesn't support gossip will help protect you and your colleagues from unfair rumors. But what if the gossip is about you? This is a more complicated situation, no doubt, but implementing the plan that I share in the next section will help ensure that you are unharmed.