The early translation of the Hebrew Scriptures into Greek gave us the word diathēkē which actually means 'covenant' rather than 'testament.' Through Tertullian's translation of diathēkē into Latin as testamentum, the terms Old Testament and New Testament came into general Christian use.
The books of the O.T. deal mainly with the covenant which Yahweh made with the Israelites in the wilderness.  In Jeremiah a new covenant is foretold  which Jesus later instituted,  and the books of the N.T. are the foundation documents of this covenant.
With the coming of Christ many O.T. prophecies were fulfilled; many previouly unrevealed truths disclosed, and certain aspects of the O.T. could now be explained. There is therefore i) a definite unity between the O.T.and the N.T.; we need to explore ii) the extent of O.T. authority, and iii) the interpretaion of the O.T.
1. The unity between the O.T. and the N.T.
Two important features of the covenant in the O.T. are i) the possibility of transgression with the consequence of punishment, and ii) promise and expectation. The Davidic covenant with the promise of an eternal kingdom resulted in the expectation of the coming of the Messiah, Son of David. When Jesus of Nazareth fulfilled this expectation in the N.T., He again instituted a new covenant with its expectation of the second coming of the Messiah.Thus the covenants and the expectations they create form a unifying theme throughout the Bible.
However, the expectation of the new covenant follows on that of the Old, for the prophets foretold the coming of a suffering as well as a conquering Messiah. Thus, whereas Jesus fulfilled every prophecy regarding a suffering Messiah, the Holy Spirit through the N.T. writers again confirmed the O.T. expectation of a Kingly Messiah, who will return to conquer, judge and "rule with an iron sceptre." 
The central message of the Bible, throughout both Testaments, is thus God's covenant with men. This covenant comprises three elements: i) the Mediator of the covenant, i.e. Jesus Christ the Son of God; ii) the basis of the covenant, i.e. God's grace, to which His people should respond with faith and obedience; iii) the covenant people, i.e. the Israel of God in the O.T. and the Church of Christ in the New. But He is in Himself the vital continuity between the Old and the New, and His followers were the righteous of the O.T. and formed the nucleus of the New.
2. The extent of O.T. authority
The N.T. often amplifies the Old in providing more complete revelation on certain matters. For example, the O.T. only revealed the unity of God; in the N.T. the Trinity is revealed. The God of the O.T. becomes the Father of the New; the eternal Son entered upon a new stage of existence when He became flesh; the "breath" or Spirit of God, denoting His divine power, became at Pentecost a Person, i.e. the Spirit of the glorified Jesus.
Thus the O.T. prepares for the New: what "God ... spoke of old to our fathers by the prophets" had to wait for its completion in the word which "in these last days" He has "spoken unto us by His Son."  Yet the apostles used the O.T. as their Bible when they proclaimed Jesus as the Messiah, Lord and Saviour. They found in it clear witness to Christ as the Giver of eternal life,  and a plain setting forth of the way of salvation through faith in Him. 
In their use of the O.T. they followed the example of Christ, who authorized the O.T. by quoting from most of the books of the Pentateuch and the Prophets. For example Jesus, in quoting from the book of Psalms, referred to it as "your law" and added that "the Scripture cannot be broken."  This short phrase, 'cannot be broken,' contains within it every claim for divine authority that can ever be made on behalf of the Bible.
3. The interpretation of the O.T.
The O.T. comprises a twofold revelation of God: mighty works and prophetic words. These two parts of revelation intermingle and explain each other. For example, while Moses interpreted the significance of the exodus for the Israelites, his words were vindicated by the events of the exodus. But at the same time the O.T. also recorded men's response to God's revelation, and in this way the N.T. finds practical instruction for Christians. For example, Paul interprets the reason for the record of the Israelites' rebellion in the wilderness as "for our instruction, upon whom the end of the ages has come." 
In much of the O.T. the spiritual meaning would not be clear apart from the interpretation and completion of the New. For example, the prophecies of the Old are fulfilled in the New; the sacrifices of the Old are completed and set aside by the one perfect and complete sacrifice of Christ; the levitical feasts are fulfilled in the Person and work of Christ; the law of the O.T. is superseded by God's grace in the New; the physical temple of God on earth pointed to Christ, and is replaced by the revelation of the mystery of God, "which is Christ in you, the hope of glory." 
God has progressively revealed Himself and His plan of redemption throughout the Bible. In the first covenants man had the opportunity to prove what he could do, and it ended in the unfaithfulness and failure of man. In the second covenant God proves what He can do with man when He is allowed and trusted to do all the work.
Under the old covenant there were men in whom the powers of the coming redemption worked mightily. In the new covenant there are men who are still held fast in the bondage of the old. In the epistle to the Galations, we find Paul comparing the two sons in Abraham's home to the two covenants.  Ishmael was born of a slave, after the flesh and will of man. Isaac was born of a free woman, through the promise and power of God.
If we live our lives trusting to the flesh, we will be held captive to sin and the law. "Only through faith in the promise and mighty quickening power of God" can we be made truly free "and stand in the freedom with which Christ has made us free." 
1. Exodus 24:7
2. Jeremiah 31:31
3. 1 Corinthians 11:25
4. Psalms 2:9; Revelation 19:15
5. Hebrews 1:1f
6. John 5:39
7. Romans 3:21; 2 Timothy 3:15
8. John 10:34-36
9. 1 Corinthians 10:11
10. Colossians 1:27
11. Galations 4:22-24
12. Murray, Covenants and Blessings, p.16-20
1. Douglas, J.D. (ed.) New Bible Dictionary, Leicester, England: Inter-Varsity Press, 1982.
2. Hammond, T.C. In Understanding be Men, Leicester, England: Inter-Varsity Press, 1968.
3. Henry, M. Matthew Henry's Commentary on the Whole Bible, U.S.A.: Hendrickson Publishers, 1991.
4. Murray, A. The Spirit of Christ, U.S.A.: Whitaker House, 1984.
5. Murray, A. Covenants and Blessings, U.S.A.: Whitaker House, 1984.
6. Payne, F.C. The Seal of God, Australia: Evangelistic Lit. Enterprise, 1987
7. Pearlman, M. Knowing the Doctrines of the Bible, S.A.: Gospel Publishing House, 1937.
8. Prince, D. Foundation Series, U.S.A.: Thomas Nelson Publishers, 1986.
9. Vine, N.E. Vine's Expository Dictionary of N.T. Words, U.S.A.:Hendrickson Publishers, ?
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