As has been pointed out, the expression “a new identity in Christ” does not appear in the Bible. It is a modern evangelical term. Several places in Scripture refer to believers being “in Christ” (1 Peter 5:14; Philippians 1:1; Romans 8:1).
Therefore, if anyone is in Christ, he is a new creation. The old has passed away; behold, the new has come (2 Corinthians 5:17).
Colossians 3:3 gives a little more insight: “For you have died, and your life is hidden with Christ in God.”
When we come to Christ as broken sinners, God exchanges our sin for His righteousness:
For our sake he made him to be sin who knew no sin, so that in him we might become the righteousness of God (2 Corinthians 5:21).
The book of Romans is a wonderful place to understand what it means to be free from sin and how God views us. Here are a few verses to get you started:
Romans 5:10: For if while we were enemies we were reconciled to God by the death of his Son, much more, now that we are reconciled, shall we be saved by his life.
Romans 6:6: We know that our old self was crucified with him in order that the body of sin might be brought to nothing, so that we would no longer be enslaved to sin.
Romans 8:15-16: For you did not receive the spirit of slavery to fall back into fear, but you have received the Spirit of adoption as sons, by whom we cry, “Abba! Father!” The Spirit himself bears witness with our spirit that we are children of God,
Romans 8:38-39: For I am sure that neither death nor life, nor angels nor rulers, nor things present nor things to come, nor powers, nor height nor depth, nor anything else in all creation, will be able to separate us from the love of God in Christ Jesus our Lord.
Romans 12:1-2: I appeal to you therefore, brothers, by the mercies of God, to present your bodies as a living sacrifice, holy and acceptable to God, which is your spiritual worship. Do not be conformed to this world, but be transformed by the renewal of your mind, that by testing you may discern what is the will of God, what is good and acceptable and perfect.
And here is the best news of all – having been chosen by God and adopted into His family, the refining work that started when we came to saving faith in Christ Jesus will reach completion:
And I am sure of this, that he who began a good work in you will bring it to completion at the day of Jesus Christ (Philippians 1:6).