The words 'covenant, testament, and will,' can all be interchangeable. The New Testament tells all about the New Covenant: the contract for the disposition of an inheritance, i.e., the will.
"Now the God of peace, that brought again from the dead our Lord Jesus, that great shepherd of the sheep, through the blood of the everlasting covenant." Hebrews 13:20
God made a number of divine covenants with the Jews in the Old Testament when their sins were forgiven under the law through animal sacrifices. The "wages of sin" were death. These animal sacrifices were acceptable to God as temporary covering for their sin, but they had to be repeated on a regular basis. These sacrifices were only shadows of the new and "better covenant" (Heb. 7:22; 8:6).
The New Covenant provided the means by which Jesus' blood sacrifice actually paid the full price to atone for our sin. Under this new will God's Plan was fulfilled: "I will put my laws into their mind, and write them in their hearts:...and their sins and their iniquities will I remember no more." Jeremiah 31:33-34. No other sacrifice would ever be required. Jesus paid it all ... once, for all time.
The old law was thus fulfilled and animal sacrifices were ceased, no longer needed. The actual 'veil' in the Jewish Temple, which closed off the area of the Holy of Holies, was actually supernaturally torn in half at the crucifixion, signifying the New Covenant.
The inheritance is eternal ... because the covenant is everlasting. Jesus now sits at the right hand of the Father and "he ever liveth to make intercession" for all those who "come unto God by him." Heb. 7:25
The gift of eternal life is our present possession if we have believed. The Holy Spirit lives in us, we have been born (again) into His family, and our citizenship is now in heaven. He is preparing a place for us: "And if I go and prepare a place for you, I will come again, and receive you unto myself; that where I am, there ye may be also." And that's what we are waiting for, and expect, very soon.
No matter how many times I think of, and study, the entire story I will never be able to entirely plumb the depths of it.
It is truly the greatest story ever told. And it's our job to tell it.