For the law was given by Moses, but grace and truth came by Jesus Christ.
The New Testament is "grace and truth."
The Law points to my need for the atonement of Jesus for my sins on the Cross.
When I believed on Jesus for the forgiveness of sins, the New Testament became mine. All the promises of God in Jesus are mine. Grace and truth is for believers, not unbelievers. How dare mockers and scorners of the Word claim these promises! Many of these consider themselves Christians! And for the scores of sincere but unconverted professors of faith in the churches, I urge you to read the book of Hebrews, which is a warning against coming up short of actual faith in Christ.
The warning of Hebrews is that many in the churches are committing the same error as the Israelites who, delivered by God out of Egypt, perished in the wilderness due to unbelief. Through the Cross all of us are afforded deliverance out of the world (Egypt). But you must believe the gospel in order to receive the benefit, otherwise it is merely "a gift never received." The only way the gift of God is received is through faith.
So the New Testament is for believers. Only believers on the Lord Jesus Christ are under grace.
For all others, you remain under the Law. You are not free of it. No, you are condemned by it. For those of you who have not believed, the wrath of God abides on you, Jn. 3:36. (John 3:16 is for believers; John 3:36b is for everyone else.) That is, God's wrath is on you right here and now. Now I know this will offend the sensibilities of some. But that is an endemic problem in Christendom--many have a form of godliness but deny its power.
I would urge any of you still under the Law to continue reading the Old Testament until you see your need of throwing yourself at the feet of Jesus Christ for the forgiveness of your sins. Jesus is the fulfillment and the end of all the Old Covenant sacrifices. Then, and only then, the New Testament is yours!