If a Rabbi does an aveirah, is it an obligation to rebuke them? Any pointers?
ב"ה Shalom There are some aspects of your question which are relevant to every person who sins and some particular to a Torah scholar. The Gemara Baba Metzia 31a, says the Mitzva of "Tochecha" =rebuke applies both from Rabbi to student and from student to Rabbi. The Rambam in Sefer Hamizvot, Mitzva 205, writes that the mitzvah of rebuke applies to the more respected person and less respected person all alike. However, the Rambam also says that when giving rebuke it must be done discreetly and in and a soft manner. (רמב"ם הלכות דעות פרק והלכה ז) The "special treatment" given to a Torah scholar who has done a wrongdoing is the way we tell the Rabbi. "Rabbi, Haven't you taught us that such and such is forbidden" (רמב"ם הלכות תלמוד תורה פרק ה הלכה ט) Furthermore, in the Talmud, (Berachot 19a) it states that when we see a Torah scholar sin at night, we should not think about him during the day (that he is continuing the sin) since our default assumption is that the Torah scholar has done Teshuva. Rabbi Menashe Klein zt"l , wrote( in his Responsa Mishne Halachot 7: 97) that this Gemara applies to any person who learns Torah. These are general rules which I've collected form sources in the Talmud and Rambam. How to apply this in your particular situation, is something that requires proper thought and tact, in order to arrive at a proper solution and remedy. All the best.