How does God mediate in the New Covenant?

Hebrews 8:6-13 KJV

[6] But now hath he obtained a more excellent ministry, by how much also he is the mediator of a better covenant, which was established upon better promises. [7] For if that first covenant had been faultless, then should no place have been sought for the second. [8] For finding fault with them, he saith, Behold, the days come, saith the Lord, when I will make a new covenant with the house of Israel and with the house of Judah: [9] Not according to the covenant that I made with their fathers in the day when I took them by the hand to lead them out of the land of Egypt; because they continued not in my covenant, and I regarded them not, saith the Lord. [10] For this is the covenant that I will make with the house of Israel after those days, saith the Lord; I will put my laws into their mind, and write them in their hearts: and I will be to them a God, and they shall be to me a people:

[11] And they shall not teach every man his neighbour, and every man his brother, saying, Know the Lord: for all shall know me, from the least to the greatest. [12] For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more. [13] In that he saith, A new covenant, he hath made the first old. Now that which decayeth and waxeth old is ready to vanish away.