Romans 3:21 — But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets.
But now — This is a favorite phrase of Paul's when he has pointed out the gloom of man's position but is about to show God's remedy and a dispensational change.
Righteousness of God = Christ Himself
Without the Law — apart from the Law. At the cross with no regard to the Law.
Manifested — the tense used refers to something that has happened in the past but still continues.
Law and prophets — The provisions of the Law (sacrifices) and the actions of the prophets bear witness to a righteousness apart from the Law. "Law and prophets" also refers to the entire Old Testament as in "The Old Testament points to the righteousness that is in Christ."