Christian peace does not mean tranquility. It means we have changed sides in the battle.
We have changed sides because we are no longer at war with God. The peace we have is reconciliation with God. But we are still at war so we still experience life as a battle. Indeed we often experience more turmoil because we can no longer simply acquiesce to the world, the flesh and the devil.
This, I think, is how we should read the promises of peace in the New Testament. We are not promised tranquility. Indeed in John 16:33 Jesus says that in this life we will have trouble. But we have the joy of knowing that through the cross we are now at peace with God. He was our enemy, coming against us in judgment. But now he is our friend and our Father. And that means we can rest from our striving for righteousness and the fear of judgment.
Take, for example, Philippians 4:6-7: ‘Do not be anxious about anything, but in everything, by prayer and petition, with thanksgiving, present your requests to God. And the peace of God, which transcends all understanding, will guard your hearts and your minds in Christ Jesus.’ Paul is not promising an easy life or even feeling of serenity. He is saying that knowing that we are been reconciled with God – and therefore that God is now for us – will guard our hearts from anxiety.