What promise did the Old Testament saints not receive?

The promise that the Old Testament saints did not receive refers to the fullness of salvation through the coming of the Messiah, which they anticipated by faith. Hebrews 11:39-40 explains that while these patriarchs had faith and were declared righteous, they did not live to see the promised Redeemer fulfilled in Christ. They understood that the law and the sacrificial system were types pointing to the coming of the Messiah, but it was only in the New Testament with Christ’s advent that the full scope of the promises of God were unveiled, securing a greater covenant and the complete redemption for God's elect.