The New Covenant that we are under in this dispensation is clearly superior to the Old Covenant, which the Israelites served under in the Old Testament.  It was not that the law contained in that covenant, that is, the Law of Moses, was bad.  It was, in fact, holy, righteous, and good (Romans 7:12).  It was just inferior to the new law introduced by Christ.  This can be seen by the better things found in the New Covenant when compared with the Old.  We have seen that the New Covenant is better in that it constituted a plan of salvation that enables sins to be forgiven, something that the Old Law could not do (Acts 13:39).

We have also seen that the New Covenant has a better sacrifice than the animal sacrifices of the Old Testament.   While the animal sacrifices had to be offered every year, the one sacrifice of Christ was sufficient for all time (Hebrews 9:12, 28; 10:1-4, 10).  When one is cleansed by the blood of Christ, their sins are remembered no more (Hebrews 8:12).

Another thing that is better under the New Covenant is the priesthood.  Today, we have a great High Priest.

Hebrews 4:14 (NASB)
¹⁴Therefore, since we have a great high priest who has passed through the heavens, Jesus the Son of God, let us hold fast our confession.

Never was a high priest called great under the Law of Moses.  No one was worthy of such a description because they all had two unavoidable flaws that our High Priest, Jesus Christ, did not have.

First, they were mortal men who at some point died.  That would be a great disappointment to the people who grew close to the High Priest and trusted him to serve them.  One day he would be gone, and they would have to get used to another man whose character might not be as strong.  With Jesus, there is continuity because He continues in this role forever.

Hebrews 7:23-24 (ESV)
²³ The former priests were many in number, because they were prevented by death from continuing in office, ²⁴ but he holds his priesthood permanently, because he continues forever.

We do not ever have to worry about our High Priest changing.  His work continues endlessly.  What is the main work of Jesus now that He has paid the penalty for our sins?  It is making intercession for us, pleading on our behalf when we sin.   No wonder we, as Christians, can have such confidence in our salvation.  We have a great High Priest working for us.

Hebrews 7:25 (ESV)
²⁵ Consequently, he is able to save to the uttermost those who draw near to God through him, since he always lives to make intercession for them.

Second, our High Priest is separate from the rest by His sinless life.  All the priests before Him had to offer sacrifices for both the people and themselves since they were all sinners.

Hebrews 7:26-8:1 (ESV)
²⁶ For it was indeed fitting that we should have such a high priest, holy, innocent, unstained, separated from sinners, and exalted above the heavens. ²⁷ He has no need, like those high priests, to offer sacrifices daily, first for his own sins and then for those of the people, since he did this once for all when he offered up himself. ²⁸ For the law appoints men in their weakness as high priests, but the word of the oath, which came later than the law, appoints a Son who has been made perfect forever. 

Our great High Priest is the main reason we can continue to appear blamelessly before God.  It is not because we are actually blameless.  It is because we have Jesus on our side.  The one who became both the sacrifice that we desperately needed (the Lamb of God) and the priest offering the sacrifice.   What a wonderful Savior we have in Him. 

As you wind down for the night, think about these things.