There are many cases throughout the Mishnayos and Gemarra of women who one is obligated to divorce. I believe all of them are Rabbinic. I'm wondering if there's ever a case where the Torah would obligate a person to divorce their wife. While it may be a mitzvah according to some to divorce one's wife with a get, the simplest explanation of that is that it's the avenue the Torah wants a person to use when they want to end their marriage. Not that they must divorce their wife.
A potential answer is cases of forbidden marriages, such as a Yisroel to a Mamzer, or a Kohen to a Zonah. I believe marital intimacy in these cases is forbidden, and maybe potentially getting married. However, let's say they are already married, and live apart, and neither of them have an interest or requirement to get remarried. Can they stay in this state? Is this an example where there's a Torah obligation to get divorced?