The way to live as God’s people under the new covenant is the same way people lived under the old covenant: by trusting God’s promises and enduring difficulties in this world.
commended for their faith: God recognized their faithfulness (see also Hebrews 11:2).
yet they did not receive what was promised: They died before Christ's promised coming. The better promise began with Christ's sacrifice (8:3–10:18) and looks forward to the future completion of God's plan for his people.
they would be made perfect: See study notes on 5:9; 7:11. Jesus has fulfilled God's goal of bringing his people into a relationship with him.