Words Translated as Peace
In the New Testament, many usages come from the Greek root eiréné (εἰρήνη), meaning “peace,” but other words include hésuchios (ἡσύχιος) and hésuchazó (ἡσυχάζω), both of which come from the root hedraios (ἑδραῖος), or “steadfast,” and mean “to hold peace” or “be quiet” or “still.” Similarly, sigaó (σιγάω), siópaó (σιωπάω), and phimoó (φιμόω) are also used, all of which mean “quiet” or “silent.”
These are similar distinctions as in the Old Testament. Some of the usages are more mundane, such as the words for “silence” that sometimes get translated to “hold one’s peace” (Matthew 20:31; Mark 1:25 and 4:39; Luke 4:35, 14:4, 19:40, 20:26; Acts 11:18 and 12:17; 1 Corinthians 14:30; 1 Timothy 2:2, etc.). One interesting use is in Acts 18:9 when Jesus says to Paul to not hold his peace, but to be unafraid and continue preaching the gospel.
Overlap with Shalom
Notable usages come from eiréné and its forms—which share several similarities with shalom:
“Peace” is used as a greeting, especially in the epistles (Mark 5:34, Luke 7:50, John 20:19-26, Acts 16:36, Romans 1:7, 1 Corinthians 1:7, 2 Corinthians 1:2, Galatians 1:3, Ephesians 1:2, Philippians 1:2, Colossians 1:2, 1 Thessalonians 1:1, 2 Thessalonians 1:2, 1 Timothy 1:2, 2 Timothy 1:2, Titus 1:4, Philemon 1:3, James 2:16, 1 Peter 1:2, 2 Peter 1:2, 2 John 1:3, 3 John 1:14, Jude 1:2, Revelation 1:4, etc.).
And just like in the Old Testament, there is even the same mention of the irony of the commonplace talk of peace when peace is not present; Paul writes in 1 Thessalonians that judgment will come “while people are saying, ‘There is peace and security’” (1 Thessalonians 5:3, ESV).
“‘Peace’ is used as a greeting, especially in the epistles.”
Heavenly Peace
Eiréné can also be used to describe a heavenly peace and (as a result of the peace with God) the possibility of both social peace and personal peace.
Heavenly peace described in the New Testament is through Jesus, as we also see in Old Testament prophecies. Even the prophecy about John the Baptist in Luke 1:79 says he would “guide our feet into the way of peace,” referencing the teaching that he was doing to prepare people for the gospel. There are plenty of specific passages that talk about the peace that comes through Jesus and His salvation: Acts 10:36; Romans 5:1, 8:6, 15:3, 16:20; 1 Corinthians 14:33; Ephesians 2:14-17, 6:15; Philippians 4:7-9; Colossians 3:15; 1 Thessalonians 5:23; 2 Thessalonians 3:16; Hebrews 7:2, etc.).
“Therefore, since we have been justified by faith, we have peace with God through our Lord Jesus Christ.” (Romans 5:1, ESV)
“For he himself is our peace, who has made us both one and has broken down in his flesh the dividing wall of hostility by abolishing the law of commandments expressed in ordinances, that he might create in himself one new man in place of the two, so making peace, and might reconcile us both to God in one body through the cross, thereby killing the hostility. And he came and preached peace to you who were far off and peace to those who were near.” (Ephesians 2:14-17, ESV)
One of the most telling verses about heavenly peace is Colossians 1:19-20 (ESV):
“In Him all the fullness of God was pleased to dwell, and through Him to reconcile to Himself all things, whether on earth or in heaven, making peace by the blood of the cross.”
“…through Him to reconcile to Himself all things, whether on earth or in heaven, making peace by the blood of the cross…”
Social Peace
Many times in the New Testament, we are encouraged to maintain social peace, both within the brotherhood (Mark 9:50, Ephesians 4:3, 1 Thessalonians 5:13, Hebrews 12:14, James 3:17-18) and with nonbelievers (Romans 12:18, 2 Corinthians 13:11, 1 Peter 3:11):
“Finally, brothers, rejoice. Aim for restoration, comfort one another, agree with one another, live in peace; and the God of love and peace will be with you.” (2 Corinthians 13:11, ESV)
“If possible, so far as it depends on you, live peaceably with all.” (Romans 12:18, ESV) 
Sometimes the response dictates what happens next (Matthew 10:13, Luke 10:5-6, Hebrews 11:31). In fact, one of the most well-known verses about peace is about social peace, when Jesus taught,
“Blessed are the peacemakers, for they shall be called sons of God.” (Matthew 5:9, ESV)
“Blessed are the peacemakers, for they shall be called sons of God.”
Personal Peace
It is the personal peace from having peace with God that is the “peace which surpasses understanding,” according to Philippians 4:7. In fact, one of the gifts of salvation is the Spirit, and one of the fruits of the Spirit is peace (Galatians 5:22). Several verses describe this inexorable peace that comes from assurance of salvation, like Luke 2:14 and 29, Acts 9:31, Romans 2:10, 2 Corinthians 13:11, and James 3:17, and John 16:33:
“I have said these things to you, that in me you may have peace. In the world you will have tribulation. But take heart; I have overcome the world.” (John 16:33, ESV)
“Rejoice in the Lord always; again I will say, rejoice. Let your reasonableness be known to everyone. The Lord is at hand; do not be anxious about anything, but in everything by prayer and supplication with thanksgiving let your requests be made known to God. And the peace of God, which surpasses all understanding, will guard your hearts and your minds in Christ Jesus.” (Philippians 4:4-7, ESV)
Peace Amid Strife
Even though peace with God makes us peaceable toward others, following Jesus certainly doesn’t guarantee the world’s peaceableness toward us. Even though Jesus was called “the Prince of Peace” (Isaiah 9:6) and God is called “the God of peace” (Romans 15:33, Hebrews 13:20), Jesus warns in Matthew 10:34, “Do not think I have come to bring peace to the earth. I have not come to bring peace but a sword.” Again, in Luke 12:51, He asks, “Do you think I came to bring peace on Earth? No, I tell you, but rather division.”
People were expecting social peace by driving out Israel’s enemies, but that is not what Jesus came for. In fact, the believers in the first century suffered greatly because of their faith; to them, just as Jesus warned, he brought danger. In Luke 19:41-44, Jesus wept about this, knowing that things would become much harder for the people He loved: “Would that you, even you, had known on this day the things that make for peace.” In John 14, too, when describing the coming Spirit, Jesus says, “Peace I leave with you; my peace I give to you. Not as the world gives do I give to you.”
So, yes, the Bible says a lot about peace, but it is important to explore because it is often misunderstood. Though we can seek peace and pray for it (Psalm 34:14 and 122:6, Jeremiah 29:7), there will never truly be peace in the world as long as it is full of sin and brokenness (Jeremiah 9:8, 12:12, 14:19; Ezekiel 7:25; Zechariah 8:10; Revelation 6:4). However, there can be peace with God through salvation in Jesus (Psalm 55:18-20), and this assurance brings indescribable peace (1 Peter 5:14).
“There can be peace with God through salvation in Jesus, and this assurance brings indescribable peace.”
An Eternal Covenant of Peace
I would encourage you to read Isaiah 54, which describes the prophecy for God’s eternal covenant of peace. The language of sympathy is beautiful, but pay attention specifically to verses 10-13, which describes the importance of the promise of peace and the heavenly care and preparation that God is putting into your peaceful destination:
“‘The mountains may depart and the hills be removed, but my steadfast love shall not depart from you, and my covenant of peace shall not be removed,’ says the Lord, who has compassion on you. ‘O afflicted one, storm-tossed and not comforted, behold, I will set your stones in antimony, and lay your foundations with sapphires. I will make your pinnacles of agate, your gates of carbuncles, and all your walls of precious stones. All your children shall be taught by the Lord, and great shall be the peace of your children.’”
So, yes, truly it is a peace beyond understanding.