The peace Jesus promises his followers is an eternal peace for hear and now. The peace is not what the world offers it’s a peace that move beyond man’s understanding. In John 14-27 Jesus said “The Peace, I leave with you; my peace I give you. I do not give to you as the world gives to you. Do not let your hearts be troubled or afraid. For Christ knew that as followers of him we will have troubles, trials and tribulations; Yet, he reminded us in John 16:33 to be of good cheer; I have overcome the world. For with Jesus he gives the peace of God. Philippians 4:7 And the peace of God, which passes all understanding, shall keep your hearts and minds through Christ Jesus.
One of the old testment prophet that exhibited that peace was Daniel. He showed how in trials and tribulations you can have peace when you rely on God.