New Covenant Theology" (hereafter "NCT"), a supposed midway between dispensationalism and covenant theology, it is common to say that Jesus is the fulfillment of the Law for the believer. And there is a sense in which that is correct: He perfectly fulfilled the Law so that His obedience could be imputed to believers. He is also the antitype to the ceremonies of the Mosaic law. However, NCT takes it further and claims that there is no further role for the Law for the believer. Rather, it posits a new law, the law of Christ. That is false.
Let me start with the second part first, the "law of Christ." That is a biblical phrase: "Bear one another’s burdens, and so fulfill the law of Christ" (Galatians 6:2). In this case, I don't think Paul is referring to the law, per se, but rather to the specific commandment of Christ, that we love one another (John 15:12). He is not talking about a system of laws.
However, the NCT use of that phrase is selective, ignoring another use of it by Paul: "To those outside the law I became as one outside the law (not being
outside the law of God but under the law of Christ) that I might win
those outside the law" (I Corinthians 9:21). Here he explicitly denies being outside the law of God. Rather, by acting as one under the ceremonial law, he is able to evangelize those who remain under that law, that is, His fellow Jews, thus demonstrating the law of Christ, love for his neighbor, as he mentions in Galatians 6:2.
In Isaiah 42, one of the Servant passages that pointed forward to the Messianic work of Jesus, God says (Isaiah 42:21), "The Lord is well-pleased for His righteousness' sake to magnify the law and make it honorable" (emphasis mine). In the incarnation of Jehovah in Jesus Christ, He did not intend to do away with the Law, but rather to magnify it. I think that is to make it a joy to His people, rather than a burden, as it is to the unforgiven sinner (Matthew 11:28).
Also, in Isaiah 51:7, He says, "Listen to Me, you who know righteousness, the people in whose heart is My law; fear not the reproach of man, nor be dismayed at their revilings." This verse is absolutely destructive of the NCT claims regarding the Law. How so? Because of the parallel description of the new covenant in the New Testament: "This is the covenant that I will make with the house of Israel after those days, declares the Lord: I will put My laws into their minds, and write them on their hearts, and I will be their God, and they shall be My people" (Hebrews 8:10, repeated in 10:16). The promise of the new covenant is not that God will do away with the Law, but rather that He will renew our love for it and obedience to it!