Hebrews 7:22 (NKJV) by so much more Jesus has become a surety of a better covenant.
The book of Hebrews in the New Testament is all about better. Before the cross, God's children were under the law covenant. The law covenant came to be when Moses received the Ten Commandments. That covenant was straightforward---obey the commandments and be blessed.
God always has been a God of grace, wanting to be our heavenly Father. Sin limited God because He is holy. The Bible says in Exodus 33:20, "But He [God] said, "You cannot see My face; for no man shall see Me, and live." God could not fellowship with sin without destroying it.
The last book of the Old Testament, the book of Malachi, has revealed that God's children even failed to make proper sacrifices. Without redemption, God was unable to bless us. Psalm 35:27 says, "Let the Lord be magnified, Who has pleasure in the prosperity of His servant." It has always been His desire.
This is where the book of Hebrews shines. The word better is mentioned thirteen times in this book. When Scripture repeats something, God wants us to understand it. Our new covenant is BETTER!
Hebrews 6:9 says "But, beloved, we are confident of better things concerning you, yes, things that accompany salvation, though we speak in this manner." In the Old Testament, Israel could sacrifice animals for salvation; Jesus gave us salvation plus a personal relationship, this is much better.
Hebrews 7:19 says "for the law made nothing perfect; on the other hand, there is the bringing in of a better hope, through which we draw near to God." The law did not make us better people---drawing near to God does. The sacrifice of Jesus made this possible.
Hebrews 8:6 says, "He is also Mediator of a better covenant, which was established on better promises." God purges our soul of dead works (Heb. 9:14). He also gave us a new spirit. The old covenant could not provide these two benefits. These are better promises to the born-again believer.
Hebrews 9:23 (NLT) says, "That is why the Tabernacle and everything in it, which were copies of things in heaven, had to be purified by the blood of animals. But the real things in heaven had to be purified with far better sacrifices than the blood of animals." The world we live in is tainted with sin. An innocent animal made a good sacrifice, but it was still of this world. Jesus was God manifest as a flesh and blood human to become the holiest possible sacrifice.
Simply put---animal sacrifice provided God with an avenue of grace. The crucifixion of Christ was an explosion of grace. It is interesting to note; the word grace appears in the New Testament one-hundred-thirty times. The book of Hebrews teaches us the new covenant is better than the old one. The New Testament teaches us that it is all about grace. That is why He repeated grace ten times as much!