Righteousness is a gift which is given to us when we receive Christ. This righteousness consists of:
1. A perfect record – all sins forgiven, all obstacles to fellowship with God removed.
2. A new nature, one which hates sin and loves what is good.
3. The power of the holy spirit imparted to us to enable us to fulfill all the will of God.
All this is given to us when Christ comes to live in us as the Comforter. He is our righteousness, our wisdom, our sanctification, our redemption. (1 Cor 1:30; 2 Cor 5:21). Obtaining this righteousness and living this righteous life has NOTHING to do with keeping the law, it is a gift freely given to us by God, a gift of grace. When we possess this gift of righteousness, it is Christ living in us and so, Christ will live his own life in us, not by us keeping our eyes on the law, but by our keeping our eyes on Christ
“But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets; Even the righteousness of God which is by faith of Jesus Christ unto all and upon all them that believe: for there is no difference:” (Rom 3:21-22)
“I am crucified with Christ: nevertheless I live; yet not I, but Christ liveth in me: and the life which I now live in the flesh I live by the faith of the Son of God, who loved me, and gave himself for me.” (Gal 2:20)
Now that it is Christ who lives, what then, does it mean that the law has been abolished? Not at all, but what it means is that we no longer try to please and obey God in a legal way. We do not perform the will of God by focusing on keeping the law, it is no longer our governor, we are not under its dominion! Our governor now, is Christ living inside of us, not the law written on stones outside. It is not the letter, it is the spirit. We produce works of righteousness because, “not I, but Christ liveth in me.” We live in harmony with the law and in fact, we live on a level much higher than what the law required. We do not do this by seeking to obey the law, we do this by abiding in Christ and he then works in us to will and to do of his good pleasure.
So to summarize, we do not abolish or reject the law, but we have moved on to something better, while leaving the government of the law, to those who are still on that immature level.
(Source: Restoration Ministry)