From Christian perspective, the old life is the life we have before we meet or have Jesus Christ in our lives and new life is when we repent of our sins and invite or accept Jesus Christ into our lives as our Lord and Savior.
I still remember my old life, I was self centered, selfish, greedy, yet self righteous, deceived, thinking I am going to heaven based on whatever good works I have. Outwardly I looked good but I knew something wrong with me.
Then I became aware of who Jesus Christ is, where He came from, why He came into this earth as revealed in the Bible.
Further seeking of truth, revealed that I am a sinner, lost and in need of a Savior.Then finally I saw that I needed Jesus Christ and prayed that He be the Savior and Lord of my life. When this happened the Bible called this a new life. For many years, the change is not very clear to me, the change is slow, I was living up and down. To others the change that I see in them is faster.
There was a tendency to hang on to the old life or parts of it.God has been very patient with me, He gave me the desire not to give up.He wants complete surrender, for me to deny or die to self and fully embrace the new life.
New life means new life, new life means new way of living, living God's way. I realize God wants not just parts of us but whole of us. Can we do it ? yes we can with God's help ,grace and mercy through Jesus and the Holy Spirit and His words and our surrender and obedience.