The Old Testament Jew had tried to be a good man and keep the commandments because he was afraid of God, and was terrified of the punishment that breaches of the law would bring. That day has for ever gone.
Now is the time of the love of God. Now a man must try to be a good man and keep God’s law, not because he fears God’s punishment, but because he feels that he must strive to deserve that amazing love. He strives for goodness, not because he is afraid of God, but because he loves him. He knows now that sin is not so much breaking God’s law as it is breaking God’s heart, and, therefore, it is doubly terrible.
Source: William Barclay, Daily Bible Study Series, Romans 3:27-31, p. 61