It is worth knowing the original connection between Purim and Yom Kippurim. See below and the questions that need answering. Gmar Chasima Tova
We’ve all heard talk of the relationship between Purim and Yom Kippurim; in fact, the Tikkunei Zohar (Tikkun 21:57b) writes that Purim is named after Yom HaKippurim, because in the future Yom Kippur will be enjoyed and will be changed from a day of affliction to one of pleasure.
Furthermore, the Zohar understands that Esther’s action, when she voluntarily entered the king’s inner throne room to intercede on behalf of her people, was akin to the Kohen Gadol entering Hashem’s Holy of Holies on Yom HaKippurim with the ketores, incense, to petition and intercede on behalf of his people. Just as the Kohen Gadol puts on special clothing on Yom Kippur, Esther donned royal clothing before approaching Achashveirosh. And just as the Kohen Gadol enters the Holy of Holies wearing his special garments, Esther entered the inner sanctum of King Achashveirosh. And just as Esther found favor in the eyes of the king, so, too, we hope to find favor in the eyes of Hashem and to achieve forgiveness.
What comparison is there between the avodah of the Kohen Gadol on Yom Kippur and the actions taken by Esther at that critical juncture of the story of Purim? His entering the holiest place in the world – with the ketores to effect forgiveness for Yisrael – is the holiest of actions. Her entering and offering herself to the king was arguably one of tumah and defilement.
Is there anything in the method through which forgiveness is achieved on Yom Kippur that is similar to the forgiveness on Purim?