"Follow peace with all men, and holiness, without which no man shall see the Lord:" (Hebrews 12: 14)
Not just being at peace, but we are to seek peace with all men, according to this verse.
Before peace with others, we need to know that we have peace with God:
"1Therefore being justified by faith, we have peace with God through our Lord Jesus Christ." (Romans 5:1 )
How do we receive this peace with God? Not by pursuing peace with others, but realizing that God wanted peace with us, with you and me, at all costs!
How did God the Father do it? By justifying us before Himself through His Son's death and resurrection, and ascension to :
"38Be it known unto you therefore, men and brethren, that through this man is preached unto you the forgiveness of sins: 39And by him all that believe are justified from all things, from which ye could not be justified by the law of Moses." (Acts 13: 38-39)
"For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him." (2 Corinthians 5: 21)
"If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness." (1 John 1: 7)
Keeping in mind that this verse is written to unbelievers, first, we then understand the next verse in 1 John:
"My little children, these things write I unto you, that ye sin not. And if any man sin, we have an advocate with the Father, Jesus Christ the righteous: 2And he is the propitiation for our sins: and not for ours only, but also for the sins of the whole world." (1 John 2: 1-2)
Jesus is our mercy seat forevermore. He is our peace (Ephesians 2: 10), and because of His Spirit in us, we bring forth fruit: love, joy, and peace, among others (Galatians 5: 22-23)
Peace is a fruit, and holiness is a work which Jesus accomplishes in us through His Spirit, too:
"But of him are ye in Christ Jesus, who of God is made unto us wisdom, and righteousness, and sanctification, and redemption:" (1 Corinthians 1: 30)
Because He is our peace, and we have peace with Him, we in turn can pursue peace with others.