When He said, "A new covenant," He has made the first obsolete. But whatever is becoming obsolete and growing old is ready to disappear. (Hebrews 8:13)
Jesus' work has ended the old covenant and the Law of Moses.
Hebrews 8 does not say that Jesus ended the old covenant or the Law of Moses.
The word "covenant" is actually not present in that verse... it has been added by the translators to reflect their bias against the Law.
Let's see what this chapter actually says:
Now the main point in what has been said is this: we have such a high priest, who has taken His seat at the right hand of the throne of the Majesty in the heavens, a minister in the sanctuary and in the true tabernacle, which the Lord pitched, not man. For every high priest is appointed to offer both gifts and sacrifices; so it is necessary that this high priest also have something to offer. (Hebrews 8:1-3)
The writer of the letter to the Hebrews does us a great service by identifying his main point: we have such a high priest. This high priest is described in Hebrews chapter 7 and the writer says: the point is we have a high priest just like that! The author points to the Levitical priesthood as being ineffective at cleansing the conscience and forgiving sin.
But now He [Jesus] has obtained a more excellent ministry, by as much as He is also the mediator of a better covenant, which has been enacted on better promises. For if that first covenant [priesthood] had been faultless, there would have been no occasion sought for a second. For finding fault with them, He says, "BEHOLD, DAYS ARE COMING, SAYS THE LORD, WHEN I WILL EFFECT A NEW COVENANT WITH THE HOUSE OF ISRAEL AND WITH THE HOUSE OF JUDAH; (Hebrews 8:6-8)
The translators attempt to insert "covenant" again in verse 7 but the context clearly indicates we are speaking of a priesthood and in verse 8 it says "for finding fault with them"... the priesthood. The writer of Hebrews then quotes a lengthy passage from Jeremiah 31 that speaks of the New Covenant and its purposes for Israel.
The concluding verse (13) confirms that the old covenant (God's Word written on tablets of stone) will be replaced by the new covenant (God's Word written on the tablets of our heart) as promised in Jeremiah 31:33.