When men entered into covenant during Bible days, they made promises sworn with an oath. Then, they offered an animal as a sacrifice. The slain animal was cut in half. Men entering into covenant walked between the two halves. Symbolically, they were saying, may I be cut off as this animal if I keep not my word of promise.
God promised with a covenant oath. No animal was sacrificed. Instead, God's only begotten Son was the sacrifice of the everlasting covenant. God's promises to every believer are sealed in the precious blood of Jesus, known in Scripture as the Lamb of God. God's covenant promises to us as believers are guaranteed and cannot be broken. Or, as the hymn says, "standing on the promises that cannot fail."
God promised with words that are forever the same (Jeremiah 31:31-34; Hebrews 7:22; 8:7-13). Know God's covenant promises. (1) God will put His laws in our mind; (2) God will be our God and we are His people; (3) We will all know the LORD; (4) God will forgive our sins and remember them no more.
God promised through the everlasting covenant (Hebrews 13:20-21). God's promises reveal His good will. He promises with a guarantee for His people. We know Him as the LORD of our lives. LORD is God's covenant name. He forgives our sins and will remember them no more. All our sins are taken away through the blood of the everlasting covenant, at the cross of Jesus.