There is a commonly held belief in the Christian Church that to be a Christian one must live under both the Covenants laid out in the Bible. In fact a minister of religion once told me that the New Testament is just an "extension of the Old Testament." This is not the case and the New Testament itself rejects this as a fallacy. Consider what the Bible has to say:
"...I will establish a new covenant with the house of Israel and with the house of Judah, not like the covenant I made with their fathers." (Heb 8:8-9)
If the new testament is not like the old testament, then what is it like? The old testament gave us the law and showed sin for what it is. It kept man constrained under law and put man in bondage to the law.
This is not to say there is anything wrong with the old testament. It merely showed up mankind's flaws and weaknesses but did nothing to remove them, nor enable man to become perfect. The law exists because man is not perfect. The law is based on works for you must "do" what is required to gain forgiveness but can never be brought to perfection through works of the law.
Conversely the new testament is concerned with freedom rather than bondage. Through Christ we can be set free from our bondage to sin and to the law to be perfected so that we do what is right, not because it is written in the law, but because it is written into our nature. The basis of the new testament is faith, and you can only come to God under the new testament through faith in Jesus Christ.
So we see that these two testaments are quite different. One is about bondage and the other about freedom. The Bible also tells us that the Old Testament was enacted with a curse saying, "Cursed be every one who does not abide by all things written in the book of the law, and do them." (Galatians 3:10) But the New Testament was enacted with a promise, "For if the inheritance is by the law, it is no longer by promise; but God gave it to Abraham by a promise." (Galatians 3:18)
These two testaments are different from each other, but they are not opposed to one another. The Old Testament teaches the principles of righteousness showing right from wrong, but it can never make a man righteous. Whereas the promise of the New Testament is righteousness by faith for, "… the scripture consigned all things to sin, that what was promised to faith in Jesus Christ might be given to those who believe" (Galatians 3:22)
So how should a Christian approach this issue? If they try to live under the law in the Old Testament they nullify the power of the New Testament as the Bible states, "I do not nullify the grace of God; for if justification were through the law, then Christ died to no purpose." (Galatians 2:21)
Christians need move from the Old into the New. We are all born under the Old Testament in this world, but through Christ we can be reborn into the New Testament, to be "born again."
So if a person moves out of the Old Testament and into the New Testament, how should they approach the Old Testament? The writer of Hebrews provides that answer saying, "In speaking of a new covenant he treats the first as obsolete. And what is becoming obsolete and growing old is ready to vanish away." (Heb 8:13), and, "He abolishes the first in order to establish the second." (Heb 10:9)
If the Christian tries to live under both testaments they nullify the New and adulterate the Old. It just won't work. They become confused because on the one hand they are condemned as sinners for breaking the law, but on the other hand are set free from sin and the law through Christ. The Apostle Paul is so bold as to say, "You are severed from Christ, you who would be justified by the law; you have fallen away from grace." (Galatians 5:4) And yet we see in so many of the Christian religions this collision of both testaments, and thus confusion reigns.
I hope that you found something here to help you or add to your own knowledge. If you have any questions, then please feel free to contact me.