I'm partial to "appearance of impropriety" as a standard of conduct for authorities and public figures.

For example, from the Code of Conduct for United States Judges:

An appearance of impropriety occurs when reasonable minds, with knowledge of all the relevant circumstances disclosed by a reasonable inquiry, would conclude that the judge’s honesty, integrity, impartiality, temperament, or fitness to serve as a judge is impaired. Public confidence in the judiciary is eroded by irresponsible or improper conduct by judges, including harassment and other inappropriate workplace behavior. A judge must avoid all impropriety and appearance of impropriety. This prohibition applies to both professional and personal conduct. A judge must expect to be the subject of constant public scrutiny and accept freely and willingly restrictions that might be viewed as burdensome by the ordinary citizen. 

"Impropriety" in that context particularly concerns respect for law, "lending the prestige of judicial office to advance the private interests of the judge or others", and "membership in any organization that practices invidious discrimination", but different things might be emphasized in different professional contexts. Appearances undermine public confidence and give cover to genuine bad actors.

You might think of this in the spirit of integrity for consequentialists, since short-sighted consequentialism is particularly susceptible to appearances of impropriety. As an example, this standard would recommend you (at the least) recuse yourself from reviewing a friend's grant proposal. For the most part, avoiding appearance of impropriety looks like standard professional ethics.

As a community standard, I think it's also valuable to pair this with a presumption of good faith. It's important that holding someone to this standard doesn't entail accusing them of impropriety. (Justifications for judicial appearance-of-impropriety standards hold this presumption so strongly they often don't even mention the idea of giving cover to bad actors, since they couldn't possibly exist.)