Gal 2:20 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.
This book (the Bible) will keep you from sin, or sin will keep you from this book. ~ D.L. Moody
Paul is referring to his former life; this new life happened because of what Jesus did on the cross.
No Longer I Who Live, this means, “Not I, who once ate from the earth [like Adam]. Not I who was once grass, as all flesh is grass, but Christ who lives in me. That is, there lives that living bread which comes from heaven, their lives wisdom, their lives righteousness, their lives the resurrection.” On Paradise 76.
The difference between the old and new covenants is that the new covenant's blood, the blood of Christ, actually cleanses from sin.
I gave my sins to Jesus Christ, and He gave me His righteousness - Pastor Spada.