The NT doesn't claim anything wrong with the Covenant. Are you talking about the Book of Hebrews? Jeremiah 31 says nothing wrong about the Covenant either, it simply says it will improve the Covenant with "The people of Israel and Judah" (i.e. the Hebrews, definitely not referring to non-converted gentiles) by putting the Law (The same exact Law Jeremiah was familiar with) into their hearts so that they will not have to be taught. This does not imply the former was faulty, just that the second one will be more like "Training wheels" to prevent mistakes. What that means exactly is up to dispute, but those who say it's referring to a different law or one that does away with "one iota or tittle" are totally out of bounds.
That was just a type o. I usually defend the NT and just got in the habit of using NT in any preface or premise. Let me be lazy and just quote what I meant from a site.
There certainly was fault with the first covenant, but the fault was not with God or in the way He made the covenant, but with us.
Hebrews 8:8 states that He found fault
“with them.” The Law showed the way to righteousness (
Romans 8:3-4), but righteousness could only be obtained if the Law were kept perfectly (
Galatians 3:10). The fault then with the Law was that man could not keep it perfectly in order to obtain righteousness. And since the Law made no provision for the permanent forgiveness of sin (
Hebrews 10:1), another covenant had to be brought, sanctified by the blood of Christ, that could provide for our salvation.
From Hebrews 8:7, what was the fault with the first covenant? How could God make a “faulty” covenant? | Brentwood Church of Christ - Brentwood, Tennessee
It is not new laws nor even a new way to be righteous but in how laws are apprehended and a final permanent solution to the problem with the first arrangement which it was only a type and shadow of.
I deal with claims that "The Pharisees were perfect and strict in obeying the Law, therefore the Law itself was what Jesus was opposing" quite often, and it infuriates me each time. There really are people that insane/moronic/militantly ignorant/dishonest, plenty. In fact, they may constitute the majority of apologists.
My entire faith is built on the fact no one has ever obeyed the law perfectly and no one ever will except Christ. I believe in grace from first to last so I hope I did not infuriate you further.
Bonus:
Matthew Henry's Concise Commentary
8:7-13 The superior excellence of the priesthood of Christ, above that of Aaron, is shown from that covenant of grace, of which Christ was Mediator. The law not only made all subject to it, liable to be condemned for the guilt of sin, but also was unable to remove that guilt, and clear the conscience from the sense and terror of it. Whereas, by the blood of Christ, a full remission of sins was provided, so that God would remember them no more. God once wrote his laws to his people, now he will write his laws in them; he will give them understanding to know and to believe his laws; he will give them memories to retain them; he will give them hearts to love them, courage to profess them, and power to put them in practice. This is the foundation of the covenant; and when this is laid, duty will be done wisely, sincerely, readily, easily, resolutely, constantly, and with comfort. A plentiful outpouring of the Spirit of God will make the ministration of the gospel so effectual, that there shall be a mighty increase and spreading of Christian knowledge in persons of all sorts. Oh that this promise might be fulfilled in our days, that the hand of God may be with his ministers so that great numbers may believe, and be turned to the Lord! The pardon of sin will always be found to accompany the true knowledge of God. Notice the freeness of this pardon; its fulness; its fixedness. This pardoning mercy is connected with all other spiritual mercies: unpardoned sin hinders mercy, and pulls down judgments; but the pardon of sin prevents judgment, and opens a wide door to all spiritual blessings. Let us search whether we are taught by the Holy Spirit to know Christ, so as uprightly to love, fear, trust, and obey him. All worldly vanities, outward privileges, or mere notions of religion, will soon vanish away, and leave those who trust in them miserable for ever