What does God promise to do with Israel's sins in the new covenant?
God promises to forgive Israel's iniquity and remember their sin no more. In the new covenant, He will put His law in their inward parts and write it on their hearts; He will be their God, and they shall be His people.
Les explains that this new covenant is not the covenant God made with their fathers when He took them by the hand to bring them out of Egypt, which they broke. Instead, God will make a new covenant with the house of Israel and with the house of Judah after those days. He will put His Law in their inward parts and write it in their hearts. He will be their God, and they shall be His people. Les connects this to Zechariah's prophecy that a surviving remnant—one-third—will suddenly realize Jehovah is their God and recognize Jesus of Nazareth as their Messiah. God will call them My people once again, though He does not call them that today. No longer will they teach every man his neighbor or brother to know the LORD, for they shall all know Him, from the least to the greatest. The reason is that God will forgive their iniquity and remember their sin no more. Les notes this is Israel's future, but only a remnant; the rest will be cut off and die, as Zechariah says.
And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more.