No new convenant is written on the Christian's heart. That is a promise made to Israel (Heb.8:8, Jer.31:31) for the Millnennial reign of Christ.
On the contrary, the Christian is commanded to remain under the control of the Holy Spirit, to 'yield to him' and not to sin (Rom.6:16,19) and to grow from being a 'babe in Christ' to an adult by going from the milk (1Pet 2:2) to meat (Heb.5:14) of the word of God.
Christians are part of spiritual Israel.
In Romans 11, Paul compares Israel to natural branches of God's promises and gentiles as branches "grafted" on to that promise.
When Jesus said the "whole law" and the prophets hang up on the law of love, he was referring to the 10 commandments.
Paul understood this concept:
2Co 3:3 Being manifested, that you are the epistle of Christ, ministered by us, and written: not with ink but with the Spirit of the living God: not in tables of stone but in the fleshly tables of the heart.
He clearly made a comparasion between the letters written on the tables of stone with God's finger, the 10 commandments, to letters written in our hearts by God.
Though I do agree that there will be a thousand year kingdom and that the law will be at that time written in everyones heart.