Walking in the Spirit causes one to fulfill the law of God, as Romans 8:4 proves. 1 John 3:4 says that sin is the transgression of the law- and we sure do not have a right to continue in sin that grace may abound. God forbid! (see Romans 6). We're not under the law in the sense that we are not under the ceremonies of the Law of Moses (and only because these were shadows of Christ who has now come as the ultimate substance of these things). A faithful believer who is abiding in Jesus and being saved from their sins (i.e. transgressions of the law) is also not under the law in the sense that the law no longer condemns them because they are rightly related to Christ. Since they are under His Lordship (i.e. righteous government) they are submitted to His Law; and since He is their redeemer and High priest God no longer counts their previous transgressions against them through His blood atonement- hence they are reconciled to God and His Law.
Every passage in the New Testament about not being under the law is dealing with these things. Jesus upheld and vindicated the morality in the law of Moses and the Old Testament as a whole (Matthew 5:17-20, Matthew 7:12, etc). The Law of Christ is the moral law of God plus whatever ceremonial ordinances God has ordained for New Covenant Christians (like baptism and the Lord's Supper). To seek the real Jesus means to do seek to do right in God's eyes; and that means coming in agreement with and striving to be faithful to God's Law. Jesus said that workers of lawlessness will be shut out of His kingdom (Matthew 7:21-27, Luke 13:23-27, etc).
Revelation 22:13-15 "I am Alpha and Omega, the beginning and the end, the first and the last. Blessed are they that do his commandments, that they may have right to the tree of life, and may enter in through the gates into the city. For without are dogs, and sorcerers, and whoremongers, and murderers, and idolaters, and whosoever loveth and maketh a lie."
Romans 3:31 "Do we then make void the law through faith? God forbid: yea, we establish the law."