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High level review:
Chapter 7 of Hebrews emphasizes the prayers and perfect character of Jesus our High Priest. Chapter 8 summarizes the significance of these truths. These chapters serve as a foundation for new hope because Jesus was a new leader who authored a new covenant.
A New Leader (vv. 1–6): Jesus was a new leader who worked in heaven at God’s right hand and offered an effective sacrifice for sin (vv. 1–3). The priestly service of Jesus was effective in supporting a new covenant (vv. 4–6).
A New Agreement (vv. 7–13): Jesus produced a new agreement for His people because the old covenant was ineffective (v. 7). This new covenant promised new power, new closeness to God, and a fresh experience of forgiveness (vv. 8–12). The result of this covenant was the superiority of the new over the old covenant (v. 13). The first covenant was made obsolete and is disappearing.