New Covenant of Grace

Jeremiah 31:31-34. 
31 “Behold, the days are coming, says the Lord, when I will make a new covenant with the house of Israel and with the house of Judah—   33 But this is the covenant that I will make with the house of Israel after those days, says the Lord: I will put My law in their minds, and write it on their hearts; and I will be their God, and they shall be My people. 34 No more shall every man teach his neighbor, and every man his brother, saying, ‘Know the Lord,’ for they all shall know Me, from the least of them to the greatest of them, says the Lord. For I will forgive their iniquity, and their sin I will remember no more.”

Hebrews 9:14-15   14 how much more shall the blood of Christ, who through the eternal Spirit offered Himself without spot to God, cleanse your conscience from dead works to serve the living God? 15 And for this reason He is the Mediator of the new covenant, by means of death, for the redemption of the transgressions under the first covenant, that those who are called may receive the promise of the eternal inheritance. (See Hebrews 8 also)

God's new covenant in Christ is not one of following rules of the Law to earn a place in His favor, but rather to find God's favor undeservedly in Christ and so have a place by His favor (grace).  We then can know God intimately, not just have knowledge about Him.  We have eternity promised us by nothing earned, only given us.  The depth of this grace should move us to run after Him, not our own goals.