What is the new normal?
1. The new covenant has a better priesthood than the old covenant, since there is no longer any need for a continual change of priests due to death (Heb 7:23). One continual priest now lives forever to make intercession before God on behalf of his people (7:24, 25).

2. The new covenant priest is better than those of the old covenant, since Jesus does not have to offer sacrifices continually for his own sins and then for the sins of his people. He has instead made one complete and perfect offering (7:27; 9:25–28; 10:12).

3. The new covenant has a better sacrifice than the old covenant; what the blood of bulls and goats could not do, since the atonement they brought could at best be only partial (10:2, 3), the blood of Christ has done once for all (9:11–14; 10:1–10).

4. Whereas the old covenant was imperfect (8:7) and thus became obsolete (8:13), the new covenant is perfect and eternal (13:20).

5. Whereas the old covenant provided a believer with no direct access to God (9:6–8), the new covenant provides a direct access to God that can purify and perfect the believer’s conscience (cf. 9:14 with 9:9).

6. The new covenant has a better guarantee, an oath sworn by God himself (7:20–22).

7. The new covenant assures the presence of the Holy Spirit in the life of each believer. The new covenant community has been touched by the promised Spirit (6:4) who, according to Paul, is both the seal and guarantee of their inheritance (see 2 Cor 1:22; 5:5; Eph 1:13, 14).

(Baker Encyclopedia of the Bible)