Rom. 8:3-4 For God has done what the law, weakened by the flesh, could not do. By sending his own Son in the likeness of sinful flesh and for sin, he condemned sin in the flesh, in order that the righteous requirement of the law might be fulfilled in us, who walk not according to the flesh but according to the Spirit. How is the righteous requirement of the law fulfilled in believers? I believe it is a mistake to believe this passage is referring to the actual performance of believers in keeping God’s law. Since that takes perfection, it is impossible for believers to be successful law keepers and that is why Paul calls it a ministry of death. Seems to me this passage is referring to the fact that Jesus kept the law and it is fulfilled in those who walk according to the Spirit, which describes believers. A chapter earlier Paul said, Rom. 7:6 But now we are released from the law, having died to that which held us captive, so that we serve in the new way of the Spirit and not in the old way of the written code.
Therefore, we are released from the law of sin and death and set free by the Spirit of life (Rom. 8:2). The bottom line of this passage is that God sent his son to do what we cannot do and that is to fulfill the righteous requirement of the law for those who, through faith, serve in the new way of the Spirit. To think that this passage is teaching successful law keeping by believers is to miss the point that Jesus Christ successfully kept the law in order that those who are in him through faith might be covered in his righteousness, not ours.
Believers should rejoice in being free in Jesus Christ and following the lead of the Holy Spirit rather than submitting to the Old Covenant yoke of slavery through law keeping.