As pointed out here >> Do blessings and curses transcend the covenants? ,the new covenant, or Christian covenant is a continuation of the old Israelite covenant.
Jesus did not abolish the Israelite Covenant and Moral Law but came to fulfil them, Matt 5:17-20, Gal 3:21. The moral law still applies to Christians BUT Jesus fulfils the Levitical and Davidic covenants by being the eternal High Priest and the eternal king of the kingdom of heaven.
One of the best summaries of the New Covenant is found in 1 Peter 1, 2.
- The promise: Salvation by grace through the promised Messiah, 1 Peter 1:3-12, 20,
- Moral Requirements: holiness (1 Peter 1:15), Purity (v22), Obey the truth (v22), love (v22), “rid yourselves of all malice and all deceit, hypocrisy, envy, and slander of every kind” (1 Peter 2:1), abstain from sinful desires (1 Peter 2:11), submit to civil authorities (v13-17), see also Rom 13:1-7, etc. [To this list could be added the many other references to the moral code in the NT such as: Matt 22:34-40, Matt 4:10, 1 John 5:20, Acts 17:29, 1 Tim 6:1, Mark 2:27, 28, Acts 16:13, Eph 6:1-3, James 2:11, Matt 19:18, Rom 13:9, Eph 4:28, Rom 7:7, etc.]
- Sacrifice: Blood of Jesus, 1 Peter 1:18, 19
- Purpose: “But you are a chosen people, a royal priesthood, a holy nation, God’s special possession, that you may express the praises of him who called you out of darkness into his wonderful light … Live such good lives among the pagans that, though they accuse you of doing wrong, they may see your good deeds and glorify God on the day he visits us.” 1 Peter 2:9, 12 - Compare Ex 19:5, 6 which Peter quotes and then expands into the application for our day until the Lord returns!
This is quintessential covenant language and uses the same structure and function as the old Israelite covenant. Jesus made the same point in Matt 21:43, “Therefore I tell you that the kingdom of God will be taken away from you and given to a people who will produce its fruit.” See also Gal 3:29, “If you belong to Christ, then you are Abraham's seed, and heirs according to the promise”.
[Note: I have deliberately avoided a discussion of Rev 5:10 as this appears couched in terms that are still future, and, because it is highly controversial. Nevertheless, it certainly quotes Ex 19:5, 6.]