Even while keeping the old covenant, Jesus also exemplified and taught his disciples how to live out the new covenant. Just like Moses before him, Jesus explained the covenant requirements prior to ratifying the covenant with a blood sacrifice. Following Christ’s example means embracing the future kingdom culture as a foretaste of what is to come.
1. New Covenant Review
Jeremiah 31.33–34 For this is the covenant that I will make with the house of Israel after those days, declares the LORD:
- I will put my law within them,
and I will write it on their hearts.
- And I will be their God,
and they shall be my people.
- And no longer shall each one teach his neighbor and each his brother, saying, ‘Know the LORD,’
for they shall all know me, from the least of them to the greatest, declares the LORD.
- For I will forgive their iniquity,
and I will remember their sin no more.”
Comments on #1: “write it on their hearts”
NET: “Two contexts are relevant for understanding this statement. The first context is the Mosaic covenant, which was characterized by a law written on stone tablets (e.g., Exod 32:15-16; 34:1, 28; Deut 4:13; 5:22; 9:10) or in a “book” or “scroll” (Deut 31:9-13). This material could be lost (cf. 2 Kgs 22:8), forgotten (Hos 4:6), ignored (Jer 6:19; Amos 4:2), or altered (Jer 8:8). The second context is the repeated fault that Jeremiah has found with their stubborn (3:17; 7:24; 9:14; 11:8; 13:10; 16:12; 18:12; 23:17), uncircumcised (4:4; 9:26), and desperately wicked hearts (4:4; 17:9). Radical changes were necessary to get the people to obey the law from the heart and not just pay superficial or lip service to it (3:10; 12:2). Deut 30:1-6 and Ezek 11:17-20 with 36:24-28 speak of these radical changes. The LORD will remove the “foreskin” of their heart and give them a circumcised heart, or take away their “stony” heart and give them a new heart.” 
J. A. Thompson: “Yahweh himself proposes to bring about the necessary change in the people’s inner nature which will make them capable of obedience. He will set his law (tôrâ) within them and write it on their hearts, that is, on their minds and wills…[T]here could be no obedience and no recognition of Yahweh’s sovereignty as long as the covenant was externalized. It needed to touch the life deeply and inwardly in mind and will.” 
Comments on #3 “they shall all know me”
J. A. Thompson: “The extent of the transformation in those days would be that intermediaries like Moses, priests, prophets, teachers, would no longer be needed to instruct people and say “Know Yahweh,” because all of them shall know (yāḏaʾ) him, young and old, from the least to the greatest. The verb know here probably carries its most profound connotation, the intimate personal knowledge which arises between two persons who are committed wholly to one another in a relationship that touches mind, emotion, and will.” 
Summarizing Jeremiah 31.33-34
- heart to obey
2. Jesus, New Covenant Exemplar
- Did Jesus have a heart to obey?
“I will put my law within them, and I will write it on their hearts.” (Jer 31.33a)a. John 4.34; 5.30
- Was Jesus loyal to his God?
“And I will be their God, and they shall be my people.” (Jer 31.33b)a. Matthew 4.8–10; Mark 1.11; 9.73. Did Jesus have intimate knowledge of God?
“And no longer shall each one teach his neighbor and each his brother, saying, ‘Know the LORD,’ for they shall all know me, from the least of them to the greatest, declares the LORD.” (Jer 31.34a)a. Matthew 11.27; John 10.14-15
4. Did Jesus have forgiven sins?
“For I will forgive their iniquity, and I will remember their sin no more.” (Jer 31.34b)
a. Hebrews 4.15; Mark 2.5, 10; John 20.23
Jesus embodied the age to come in lots of ways: when he began his ministry (Luke 4.21), when John’s disciples came to ask if he was the messiah (Luke 7.22), when the Pharisees said he cast out demons by Beelzebul (Matthew 12.28), when he received the spirit, when he restored outcasts from society, when he healed the sick and raised the dead. Encountering king Jesus gave you a taste of the kingdom. There was a kingdom bubble wherever he went.
Mark 2.18-22 His ministry had a distinctive newness to it.
“The meaning of the saying new wine is poured into new skins is that the presence and teaching of Jesus was something new and signaled the passing of the old. It could not be confined within the old religion of Judaism, but involved the inauguration and consummation of the kingdom of God. 
“The presence of Jesus inaugurates the messianic time of joy when fasting is rendered superfluous, so long as he is in the midst of his people. The images of the wedding, the new cloth and the new wine are distinctly eschatological in character, like that of the messianic banquet in Ch. 2:15–17…They stress the element of fulfilment which is marked by the presence of Jesus. His person is both the sign that the old situation has been radically altered and the pledge that the reality described by these images shall be experienced in the appropriate time. 
3. Jesus, New Covenant Teacher
Moses taught the old covenant before he ratified it.
Moses lived the old covenant as an example.
Jesus taught the new covenant before he ratified it.
Jesus lived the new covenant as an example.
Jesus taught & lived out new covenant while also obeying old covenant, because he lived during the overlap. He was still obligated to keep old while also bringing out new.
Even so, it’s clear that Jesus was a new Moses, bringing the new covenant teaching to God’s people. For example, in the Gospel of Matthew, we find five blocks of teaching, just like the five books of the Torah.
- Matthew 5-7
- Matthew 10
- Matthew 13
- Matthew 18
- Matthew 23-25
Jesus’ signature lifestyle teaching—the Sermon on the Mount (Matthew 5-7)—provides a ready summary of new covenant commands.
NT Wright: “God is acting in a through Jesus to turn the world upside down, to turn Israel upside down, to pour out lavish ‘blessings’ on all who now turn to him and accept the new thing that he is doing. (This list is sometimes called ‘the Beatitudes,’ because the Latin word ‘beatus’ means ‘blessed.’) But the point is not to offer a list of what sort of people God normally blesses. The point is to announce God’s new covenant.
In Deuteronomy, the people came through the wilderness and arrived at the border of the promised land, and God gave them a solemn covenant. He listed the blessings and the curses that would come upon them if they were obedient or disobedient (chapter 28). Now Matthew has shown us Jesus, coming out of Egypt (2.15), through the water and the wilderness (chapters 3 and 4), and into the land of promise (4.12-25). Here, now, is his new covenant.
…[T]hose who follow Jesus are to begin to live by this rule here and now. That’s the point of the Sermon on the Mount, and these ‘beatitudes’ in particular. They are a summons to live in the present in the way that will make sense in God’s promised future; because that future has arrived in the present in Jesus
…Throughout this chapter, Jesus is not just giving moral commands. He is unveiling a whole new way of being human. No wonder it looks strange. But Jesus himself pioneered it, and invites us to follow.”
In Christ, all the covenants find their fulfillment.
Stephen Wellum: “In Jesus’s life and work, the desperate plight begun in Eden now finds solution, and the new creation begins to dawn…In fact, the conception of Jesus is evidence that in him the new creation has come; literally, Jesus is the first man of the new creation…Thus, all that Jesus taught, all the miracles he performed, and all that he accomplished in his cross work was tied to the dawning of God’s kingdom, which in turn, is bound up with the fulfillment of the covenants and the inauguration of the new covenant age.”
The new covenant lifestyle is the way of the kingdom. This is exciting as we can live out the future now, and give the world a foretaste of what is to come, just like Jesus did
4. Preparing Disciples for the Spirit
Not only does Jesus exemplify the new covenant lifestyle and explain how to live it out, he also prophecies the outpouring of the spirit on his disciples to equip them to be new covenant people.
John 14.15–17 When the spirit comes, it will enable them to keep his commandments.
We will return to the spirit later to see how integrally tied it is to the new covenant.
W. Hall Harris, eds. The NET Bible Notes. 1st, Accordance electronic ed. (Richardson: Biblical Studies Press, 2005), paragraph 54363.
J. A. Thompson, The Book of Jeremiah, (Grand Rapids: Eerdmans, 1980), 581.
W. Hall Harris, eds. The NET Bible Notes. 1st, Accordance electronic ed. (Richardson: Biblical Studies Press, 2005), paragraph 67466.
William L. Lane, The Gospel of Mark, New International Commentary on the New Testament. Accordance electronic ed. (Grand Rapids: Eerdmans, 1974), 112.
 N. T. Wright, Matthew for Everyone (Louisville: Society for Promoting Christian Knowledge, 2004), 37-38, 49.
 Peter J. Gentry and Stephen J. Wellum, Kingdom through Covenant, 2nd ed. (Wheaton, IL: Crossway, 2018), 714, 716, 719.