WE HAVE A BETTER COVENANT BECAUSE it is established on better promises

“But now He has obtained a more excellent ministry, inasmuch as He is also Mediator of a better covenant, which was established on better promises.” (Heb. 8:6 NKJV)

Covenant:  is a contract or agreement between two parties. The word is used with reference to God's revelation of himself in the way of promise or of favor to men. – Bible Dictionary

A new covenant in the blood of Jesus which is poured out for you

Our New Testament covenant is better than the Old Testament covenant because it’s paid for by the blood of Christ. 

“In the same way, after supper He took the cup, saying, "This cup is the new covenant in My blood, which is poured out for you.” (Luke 22:20)

“…to Jesus the mediator of a new covenant, and to the sprinkled blood that speaks a better word than the blood of Abel.” (Heb. 12:24)

Jesus became the guarantee of a better covenant that made the old covenant obsolete

We have a better covenant than the old one because it is guaranteed by Jesus. 

“Because of this oath, Jesus has become the guarantee of a better covenant.” (Heb. 7:22)

“By speaking of a new covenant, He has made the first one obsolete; and what is obsolete and aging will soon disappear.” (Heb. 8:13)

Therefore…

“Therefore Christ is the mediator of a new covenant, so that those who are called may receive the promised eternal inheritance, now that He has died to redeem them from the transgressions committed under the first covenant.” (Heb. 9:15)