Heb 10:9 Amp says it a little differently.
“He then went on to say, Behold, [here] I am, coming to do Your will. Thus He does away with and annuls the first (former) order [as a means of expiating sin] so that He might inaugurate and establish the second (latter) order.
I read that to say that what’s being inauguarated is a “new” way of dealing with sin .. the old way of shedding the blood of goats and lambs is no longer the “order”, but the new order is through the blood of Jesus.
So again .. I cannot see within that scripture that it says the “old covenant” no longer exists, but only that the old way of the shedding of blood, has been replaced with the sacrifice of Jesus’ blood.
Myabe I’m not reading it right .. but I have it underlined and a note in my margin (from class), that it was the “order” that was taken away .. not the “old covenant”.
God promised the Jews that when the Messiah came, He would write the law on their hearts and "give them a soft heart instead of their stony one of sin".
This idea of the Messiah going to come was a big deal for the ancient Jews. They thought about it all the time.
Think of how big a deal it was for Abraham, from whose seed the Messiah would come -- think about how Abraham sacrificed this son of the Promise on the mountain top in such agony!
The ancient Jews were saved because they believed God was going to send the Messiah in the FUTURE.
This is why Paul writes about the faith of the Jewish forefathers having saving faith. They were those who Jesus tells us "who longed for this day but did not live to see it."
I'm not a big NIV fan but this is from the Old Covenant, Jeremiah 31:33:
"This is the covenant I will make with the house of Israel after that time," declares the LORD. "I will put my law in their minds and write it on their hearts. I will be their God, and they will be my people."