Can a rabbi give Written Torah(תורה שבכתב) study classes at night?
It is permitted for the Rabbi to give classes in the written Torah at night. First of all halachically it is permitted even to read the written Torah at night. Even those who say that it shouldn’t, agree that if it can’t be done during the day, that it is permitted. Classes that are scheduled usually have to be said their specific time. Additionally, even those who are careful about this, it is only when it is strictly the text, but not when it is studied with commentaries, therefore a class is permitted.
Shar Hatzion 239-1, Be’er Moshe 4-22, Btzel Hachochma 4-46.