chadash does mean Renew but this doesn't mean it cannot be modify to best fit those coming into it. . As was quoted
"Behold, the days are coming," saya the HaShem, "that I will make a Renewed covenant with the house of Israel, and with the house of Judah"
This renewed Covenant based on faith, hope and love. is for BOTH houses.
"Not like to the covenant that I made with their fathers in the day that I took them by the hand to bought them out of the land of Egypt; which my covenant they broke, although I was an husband unto them, says HaShem."
This covenant will not be based on the Moshe covenant of sacrificing bulls and goats and doves. one sacrifice covers all the blood sacrifices but the Thanksgiving Sacrifice (of Bread and Wine) Still stands.
33 But this shall be the covenant that I will make with the house of Israel; After those days, says HaShem, I will put my law in their minds, and write it on their hearts; and will be their God, and they shall be my people.
Note The House of Judah is not mentioned this time. This is because the House of Israel, Ephraim, though the youngest of the brothers (and uncle) according to Jer. 31.9 is HaShem's first born:
31.9 They will come with weeping; they will pray as I bring them back. I will lead them beside streams of water
on a level path where they will not stumble, because I am Israel’s father, and Ephraim is my firstborn son.
And Ezekiel states:
Ez. 37.15 The word of the HaShem came to me: 16 “Son of man, take a stick of wood and write on it, ‘Belonging to Judah and the Israelites associated with him.’ Then take another stick of wood, and write on it, ‘Belonging to Joseph (that is, to Ephraim) and all the Israelites associated with him.’ 17 Join them together into one stick so that they will become one in your hand.
This happened in the first century. Christ first called Judah and all the disciples were Jewish. Thus the first stick is for Judah and all those associated with him (like the Tribe of Benjamin). Then Christ sent Paul to reach the gentiles and in bringing salvation to the gentiles (Joseph means He will add) he was also bringing in Ephraim (that is, to Ephraim).
Ez.37.18 “When your people ask you, ‘Won’t you tell us what you mean by this?’ 19 say to them, ‘This is what the Sovereign Lord says: I am going to take the stick of Joseph—which is in Ephraim’s hand—and of the Israelite tribes associated with him, and join it to Judah’s stick. I will make them into a single stick of wood, and they will become one in my hand.’
When people ask, ask what, when we regain interest in the first century Church, Vatican II was a call to make that return, then these stick will be joined again but look the order has changed. And another detail has changed, not only is the stick of Joseph also Ephraim, now this stick rests in Ephraim's hand, Rom.11.25-27, and this includes those tribes (the Grafted in) associated with them. Then this stick, in Ephraim hand will reunite with Judah stick in just as Judah stick reunited with Joseph's long ago.
Jer.31. 34 And they shall teach no more every man his neighbor, and every man his brother, saying, Know the L-rd: for they shall all know me, from the least of them unto the greatest of them, saith the HaShem: for I will forgive their iniquity, and I will remember their sin no more.
We are not to teach our neighbor, for Christians Judah and other Christian bodies; or our brother for Ephraim that's Judah. Besides Judah does know a form of Christ (see our write ups on Revelation on the Scripture site for details). They do not see Him as the Suffering Messiah, Moshiach ben Y'sef (Messiah Son of Joseph), or Ben Ephraim, but then this was because they missed His larger Mission.
However they do see Him in Moshiach Ben Dovid, (Messiah Son of David). Part of why they do not believe is because Jesus Christ did not fulfill everything the Messiah was to fulfill. He did not bring Ephraim home (Roman 11.25's mystery) , Yet even so He still "will forgive their iniquity, and I will remember their sin no more" for the are beloeved for their father's sake, Rom.11.28.