Translation:Tomorrow is the day to take over the department.
To take on a duty or a task is to assume responsibility. You can assume leadership also. But "take on" a department would mean to oppose it in a conflict. Take over or Take charge of would be right here. But the most natural would be "Tomorrow is the day I take charge of the department." Or we.
I mostly agree. However since we have no further context here, if a previous sentence suggests more responsibility, say:
Boss : it's time you stepped up to more management responsibility, tomorrow is the day...
Hmmm, perhaps "Tomorrow is the day of being in charge of the department", but really this sounds a little strange, at least it does without context. But "assume" in this sentence is quite simply wrong. I can't think of any context where the given translation would sound like a reasonable utterance from a native speaker.