There are two terms that I often hear people confuse: Old Covenant and Old Testament.
These two terms are not the same.
The Old Covenant refers to the particular relationship that God established with Israel on Mount Sinai (cf. Exodus 24). The Old Testament refers to the Scriptures of Israel before the time of Christ, what Jesus called “the Law and the Prophets” (Matthew 22:40) and what Paul called “the oracles of God” (Romans 3:2).
The Old Covenant is temporary and provisional. It includes land, law, temple, priesthood, sacrifices, etc. as part of God’s dealings with Israel that find their fulfillment in Christ. The Old Testament is not temporary or provisional. The books of the Old Testament form an enduring witness to God and his ways that continues to have authority alongside the New Testament.
The Bible says some things about the deficiency of the Old Covenant (cf. Jeremiah 31:31-34 and Hebrews 8:7-13). But the Bible never speaks about the deficiency of the Old Testament. Just the opposite: Jesus said if people don’t listen to Moses and the Prophets they won’t listen even if someone rises from the dead (Luke 16:31). And when Jesus rose from the dead and met a pair of confused disciples on the Emmaus road, he used the Old Testament as the way of providing the context and content for making sense of who he is. “Then beginning with Moses and all the prophets he interpreted to them the things about himself in all the scriptures.” (Luke 24:27)
Today the church does not live under the Old Covenant. But that doesn’t mean that the church does not live under the continuing authority of the Old Testament as it teaches us in its own way who God is, the shape of his salvation in Christ, the character of his people, the nature of worship, the goal of mission, etc.
Someone once told me that theology is the art of making distinctions. It is important to distinguish Old Covenant (a temporary covenantal arrangement) from Old Testament (Israel’s scriptures as an enduring theological witness).