Translation
so that the righteousness of the Law could be fulfilled in those of us who walk according to the Spirit, not according to the flesh.
Paraphrase
God did all this so that the righteousness which the Law taught and which it aspired to (but could not deliver) could be completed in us, specifically, in those of us who now live controlled by the Holy Spirit, not controlled by twisted human desires.
JESUS ACCOMPLISHED WHAT THE LAW COULD NOT
The Law does have righteousness (v. 4), meaning that it can teach righteousness and it provides a step in the right direction. However, this passage also indicates that the law is incapable and weak (v. 3). Paul demonstrates that Jesus accomplished what the sacrifices of the Law could not accomplish – true atonement for all the sins of all the people who seek it from Him in the right way.