There is not time to explore this completely, but notice that Jesus says that the Passover will not be fulfilled until the Kingdom of God. It is easy to read right over that, but it is a critical part of Passover. The sin offering has already been fulfilled (Hebrews 1:3; 7:27; 9:12-14, 26-28; 10:12, 18), but the Passover has not, as it says here. This is because of Passover's theme of redemption, which is actually a process. This is why Scripture speaks of redemption in both the past (Romans 3:23-25; Ephesians 1:7; Colossians 1:14) and future tenses (Luke 21:28; Romans 8:23-25; Ephesians 1:13-14; 4:30). We have been redeemed from the death penalty, but we still need to be redeemed from this corrupted nature that incurs the death penalty (see Titus 2:11-14). God must redeem us from this flesh - this body of death, as Paul calls it - so we can fully manifest the image of our Creator. Thus, our final redemption occurs when we have been resurrected and have fully taken on the incorruptible nature (see I Corinthians 15:50). At that point, Passover will be fulfilled.
All three synoptic gospels describe the cup as containing the blood of the covenant, as do Paul's Passover instructions in I Corinthians 11. Matthew adds here that the blood also accomplishes the remission of sins. Notice, though, that the remission of sins does not stand on its own, but it comes through the New Covenant. That covenant contains the forgiveness of sins, but also includes much more (Jeremiah 31:33-34; Hebrews 8:10-12; 10:16-18).
In His Passover prayer in John 17, Jesus includes another aspect of the New Covenant, that of knowing the Father and Him. This covenant allows for those entering the covenant to have a relationship far beyond what the previous covenant offered - to actually know the Father and the Son. Jesus calls this relationship eternal life. It is a life of abundance - foremost spiritual - that continues past the grave in the resurrection.
