“These things I have spoken to you, so that in Me you may have peace. In the world you have tribulation, but take courage; I have overcome the world.” (bold mine, John 16:33, NASB)
As one walks in obedience to God, she grows spiritually, and she experiences more of her unity with Christ. The new you is fully in Christ—fully in unity with him, but she does not experience it due to the flesh, sin, deception, and spiritual blindness. Sanctification is the transformation of our soul (thoughts and emotions) from who we used to be to who we really are (a new creation in Jesus' likeness). It is the process of removing the veil (2 Corinthians 3:14-18; Note v. 14: in Christ and v. 18: transformed into his likeness).
So we can be of good courage (going forward in spite of pain and fear), because it is God who works in us so we experience Jesus living through us more and more, and so we experience his overcoming of the world more and more. Overcoming the world is winning the battles which trouble us and in which we suffer. The result is peace, including the peace that surpasses all understanding (Philippians 4:7), because we experience more and more of our unity with Jesus, the God of all peace.