Summary: Years before Hebrews was written, God had declared there would be "New Covenant." This new legal contract had better promises than the Old one, but what is better?
OPEN: After the death of Elvis Presley it became fairly common to read headlines in the Tabloids such as: "I was Elvis’ Love Child" or "Elvis’ Ghost is My Father". Many people claimed to be related to "The King" either for the prestige of wearing his name or possibly to try and get a share of his inheritance. In the heat of all this activity, a Detroit radio station advertised that for just $2 and a self-addressed, stamped envelope, YOU TOO could be Elvis’ child.
For that sum you could receive an authentic birth certificate from the radio station signed by a Radio Disk Jockey named Dick Puritan. The certificate claimed it entitled the bearer to "appear on any talk show in the country." About 2000 people sent in their envelopes and became "children of the King."
APPLY: Everybody knew it was a worthless piece of paper. No one became Elvis’ child because of this certificate. And the people who bought those documents had no legal standing for anything.
BUT WHY? Why couldn’t you become Elvis’ child by purchasing one of those documents? Because the people at the radio station had no authority to issue the document in the 1st place.
I. What the writer of Hebrews is telling us is that there is now a legal document - a “New Covenant” - that literally makes us children of THE King.
This New Covenant is what makes us children of the King. It has value because the one who offered it had the authority to do so.
“… the ministry Jesus has received is as superior to theirs (i.e. the priests of the O.T.) as the covenant of which he is mediator is superior to the old one, and it is founded on better promises.”
This New Covenant has better promises than the Old one did. Promises? What’s this NEW Covenant offer that we couldn’t have had before?
II. First, we have a new relationship.
The Old Covenant was something you were born into. If you were born of Jewish parents, you were an Israelite. You were an Israelite because all your family had been Israelites. It wasn’t a choice that you made – it was pretty much made for you.
But to become a Christians is something else again. You can’t be born “into the church.”
You CAN be born of Christian parents and be brought to church every Sunday of your life. But you can’t be “born” a Christian just because your parents were.
You have to be reborn “of water and of the spirit” (John 3:5 (quickview) ). You have to believe that Jesus is the Christ, the Son of the Living God. You need to recognize that you are a sinner in need of forgiveness and repent of your sins. You need confess Jesus is your master, the one who will now run your life. And you need to be buried in the waters of Christian baptism and rise again to a new life.
No one else can make that decision for you. But when we’ve made that decision, Romans 8:15 (quickview)  tells us we have “… received the Spirit of sonship. And by him we cry, <"Abba,> Father.”