Peace and rest come from understanding and believing the message of grace, which is the power of the Gospel. When people truly believe that their righteousness is ONLY found in what Jesus accomplished at the cross (NOT their own performance) - they find peace, joy, and rest in Jesus Christ.
"There remains, then, a Sabbath-REST for the people of God; for anyone who enters God's REST also rests from his own work, just as God did from His. Let us, therefore, make every effort to enter that REST..." Hebrews 4:9-11
This Sabbath REST is Christ as our rest, a prize to His diligent seekers, who not only are redeemed but also enjoy him in a full way, thus becoming the overcomers.
Jesus knows that when we spend time with him, we find peace. He invites us into his presence:
“Come to me, all you who are weary and burdened, and I will give you REST. Take my yoke upon you and learn from me, for I am gentle and humble in heart, and you will find REST for your souls. For my yoke is easy and my burden is light.” Matthew 11:28-30
""In repentance and REST is your salvation, in quietness and trust is your strength" Isaiah 30:15
"You will keep in perfect PEACE those whose minds are steadfast, because they trust in you." Isaiah 26:3