For example, in 10:12-13, by quoting Psalm 110:1, the assurance of the victory of King David, he is telling us something about David's descendent, our King the Christ.
When comparing the daily sacrifice of priests with the one-time sacrifice of Christ, he writes that after offering "for all time a single sacrifice for sins, 'he sat down at the right hand of God,' and since then has been waiting 'until his enemies would be made a footstool for his feet.'"
Further, in 10:16-17, he quotes from Jeremiah 31:31-34, as he did in 8:8-12. When Jeremiah spoke, he was talking to Israel and Judah.
The message in Hebrews is intended for a broader audience. What God had promised for them then is now true for all of us:
"I have forgiven you."