Moral authority refers to the perceived credibility and righteous influence a person or entity holds in matters of right and wrong. It is the ability to guide or persuade others based on a strong sense of ethics, integrity, and principles.

a quality is a trait about a person that is good and a moral is something to learn

Answer

Good and Bad

Well, it depends on where the moral authority comes from... and whether you agree with it or not. You might call it different things, depending on those or other factors. Could be a Theocracy if the moral authority was religious... a dictatorship if it was one person making the moral calls. Democracy if the moral calls are made by everyone voting... etc. I don't think there is a separate word that means exactly that.

a pastor, elder, the BIBLE