As we approach Easter Sunday, I have been reviewing the nature of the atonement, particularly its nature and timing. I wrote a post along these lines several years ago (link), and while I agree with aspects of what I said there, I don't believe I did full justice to the relationship of Christ's resurrection to our atonement.
I said there that Christ's "sacrifice was completed, finished, and accepted by the Father upon His death." I don't believe that to be the case now. I believe Leviticus 16:17 has an antitype after all, that being the post-resurrection, post-ascension presentation of Himself in the holy place described by the author of Hebrews. There are a few reasons I think this.
Evidence that the presentation of Himself in the holy place as described by the author of Hebrews is post-resurrection and post-ascension is that it wasn't until Christ ascended after His resurrection that He sat at the Father's right hand (Mark 16:19, Acts 2:32-33, Romans 8:34, Ephesians 1:20, Revelation 3:21, etc.).
Christ's sitting at His Father's right hand is an event taken up by the author of Hebrews in connection with Christ's sacrificial work. Hebrews 1:3 and 10:12 say that after Christ made purification for sin or offered His once for all sacrifice, He sat down at the right hand of the Father. This sitting down signified the completion of His sacrifice, suggesting He so sat immediately after making purification or sacrificing. That would imply everything Christ did up to that point - beginning from, at least, the point of His death, but probably His incarnation too (if we're considering His unblemished life as necessary for an acceptable sacrifice), up until His resurrection-ascension and appearance in the holy place - was typified in the sacrificial ritual mentioned in Leviticus 16.
Leviticus 16:17 mentions atonement is made in the holy place on the day of atonement, and Hebrews 13:11-12 - which includes the significance of the burning of the sacrificial carcasses on the day of atonement to Christ's death - also notes that the sprinkling of the slain animal's blood on the mercy seat in the innermost part of the tabernacle is sacrificial, further connecting this part of the typical ordeal to Christ's antitypical one. So while the death of Christ is integral to the atonement, that seemingly isn't the end of the story. Protestants already recognize that Christ's obedience in life was necessary for atonement, but there is a need to incorporate His resurrection-ascension in His atoning work.
Several passages in Scripture also mention the resurrection in the context of Christ's substitutionary work:
2 Corinthians 5:15 He died for all, that those who live might no longer live for themselves but for him who for their sake died and was raised.
Romans 4:25 who was delivered up for our trespasses and raised for our justification.
The idea here isn't that Christ's resurrection was just a bonus, an unnecessary component of Christ's work in which we get to graciously participate because the Father decided to instantiate it rather than some other possibility. If Christ wasn't resurrected, our faith is in vain. His resurrection is part of what grounds the application of the redemptive benefits: spiritual rebirth, justification, etc. How, then?
One thing to note is that Christ's fulfillment of the day of atonement type doesn't strictly follow the temporal order of events that day, which makes sense, as Christ is both the sacrifice and He who offers the sacrifice. Hebrews 13:12 correlates Christ's death to the burning of the sacrificial carcasses. This happened after the blood of the animals was sprinkled on the mercy seat in the holy place. However, Christ's death happened before His appearance in the holy place, per Hebrews 9. So it's the essence of the type that matters, not the timing, if we are to associate Christ's resurrection-ascension with some part of the day of atonement ritual.
Is there a part of the day of atonement ritual to which Christ's resurrection-ascension corresponds? I think so. I'm still working through it, but a natural fit seems to be the reemergence of the high priest from the holy place and/or his associates into the camp after both burning the remains of the sacrifices outside the camp (to which Christ's death explicitly corresponds) and a prototypical baptism-cleansing.
How would this aspect of the atonement ritual connect with the resurrection-ascension? Because it is how [the people of God knew that] the sacrifice was acceptable to God, [that] the high priest rightly represented them, [that] their sins were indeed being atoned for, and [that] they could continue to depend on God's presence dwelling among them. Christ not only fulfills these same functions but, as a better mediator of a better covenant, goes beyond them to bring us to the most holy place of God's dwelling. The resurrection proved it.