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In chapter 7, the writer had considered the superiority of the new priesthood. It follows that such a priesthood must have a superior priestly ministry. That it does is unfolded in 8:1-10:18. In the process, the letter reveals that the New Covenant underlies this newer priestly service.
In Hebrews 8:1-5, the writer of Hebrews discusses the place of Jesus’ ministry. The “main point” of this section is the High Priesthood of Christ, mentioned in 2:17-3:1 and developed in 4:14-7:28. The author of Hebrews opened this passage with a clear transitional statement: the point of what we are saying is this. The author wished to summarize what they had been teaching and go on to new ideas. By referring to the Lord Jesus as “a high priest, who has taken His seat at the right hand of the throne of the Majesty in the heavens,” the author picked up the wording of 1:3 (cf. 10:12; 12:2).