An unsullied reputation means someone or something is respected and admired for being honest and pure.
When we talk about an unsullied reputation, we usually mean that someone has managed to keep their good name intact through all sorts of challenges. A politician might be praised for having an unsullied record on a particular issue, even after many years in office. This means they haven't been involved in any scandals or questionable dealings that could have tarnished their image. It's also possible for something like a company to have an unsullied reputation, meaning customers trust it completely and have no complaints.
Not sullied.
