The Skulener Rebbe (Rebbe Eliezer Zusia) zt’l would say that on Rosh Hashanah, Yom Kippur, and Succos, we build a beautiful (spiritual) edifice, which is the source for bounty and blessings for the new year. Yet, something is missing. There is no light!
Everyone understands that if you have a building without electricity, the building isn’t finished yet. Something essential is missing.
Similarly, the new year without light isn’t complete. Chanukah adds the light. Now the new year is complete. The light is the joy of Yiddishkeit and happiness with the mitzvos. That is the light of Chanukah, which we add into the new year.