Atonement Without the Kohen Gadol
Hello. What do rishonim and even Chazal say about the halachic matter of kapara without the activity of the Kohen Gadol in the Beis Hamikdash on Yom Kippur? I am aware of the general concept of prayers replacing sacrifices, but specifically, what is the effect of not having the kapara through the avoda of the Kohen Gadol? Do we have anything in the Oral Law that indicates the alternative (as we do in the matter of the calendar through cheshbon instead of testimony)? Thank you.