We have not brought about this righteousness by ourselves, so it is not our righteousness in that sense. While we are legally righteous before God, we are less than perfectly righteous in our living. This is where the doctrine of sanctification comes in. Sanctification is made possible by God's grace, through faith in Jesus Christ. In sanctification, God accomplishes his will in us as Christian life proceeds.
Sanctification never replaces justification.
John Calvin, a leader of the Protestant Reformation, taught that justification and sanctification are inseparable, because both come as a result of Jesus coming to live in us. We are sanctified, we are led in a new life of love and good works. Justification is thus an act of God, external to the sinner, and sanctification is the action of God within him. Justification and sanctification will be part of a Christian life. You can't have one without the other.