The unknown author of Hebrews is taking a quote from Jeremiah 31:33, and it concerns the "house of Israel" "after those days". Are you of the "house of Israel"? Does each man still go out and teach his neighbor how to "know the LORD" (Jeremiah 31:34)? Are the "days", when the whole city, and whole valley of the dead bodies, not being overthrown anymore forever (Jeremiah 31:40). Zechariah 14:1-3 prophesizes that Jerusalem will indeed be captured again. And it was overthrown numerous times after Hebrew 8:10 was written.
Not sure where your confusion is coming from here. It's talking about the new covenant between God and man. The "house of Israel" is God's people--of which I am one. For those who know God, it is no longer necessary to teach them the Law, because the Law is within them; by loving God and loving others, they automatically fulfill the Law under the new covenant.
Maybe some context will help...
"But as it now is, He [Christ] has acquired a [priestly] ministry which is as much superior
and more excellent [than the old] as the covenant (the agreement) of which He is the Mediator (the Arbiter, Agent) is superior
and more excellent, [because] it is enacted
and rests upon more important (sublimer, higher, and nobler) promises. For if that first covenant had been without defect, there would have been no room for another one
or an attempt to institute another one.
"However, He finds fault with them [showing its inadequacy] when He says, Behold, the days will come, says the Lord, when I will make
and ratify a new covenant
or agreement with the house of Israel and with the house of Judah. It will not be like the covenant that I made with their forefathers on the day when I grasped them by the hand to help
and relieve them
and to lead them out from the land of Egypt, for they did not abide in My agreement with them, and so I withdrew My favor
and disregarded them, says the Lord.
"For this is the covenant that I will make with the house of Israel after those days, says the Lord: I will imprint My laws upon their minds, even upon their innermost thoughts
and understanding, and engrave them upon their hearts; and I will be their God, and they shall be My people. And it will nevermore be necessary for each one to teach his neighbor and his fellow citizen or each one his brother, saying, Know (perceive, have knowledge of, and get acquainted by experience with) the Lord, for all will know Me, from the smallest to the greatest of them. For I will be merciful
and gracious toward their sins and I will remember their deeds of unrighteousness no more.
When God speaks of a new [covenant or agreement], He makes the first one obsolete (out of use). And what is obsolete (out of use and annulled because of age) is ripe for disappearance
and to be dispensed with altogether." --Hebrews 8:6-13 (Amplified Bible)