Not that we are adequate in ourselves to consider anything as coming from ourselves, but our adequacy is from God, who also made us adequate as servants of a new covenant, not of the letter but of the Spirit; for the letter kills, but the Spirit gives life. (2 Corinthians 3:5-6)
Scripture says that Christians are servants of a new covenant not the old covenant.
First: It is true that believers are members of a new covenant. Every believer, however, must recognize that the new covenant (as defined by Scripture) has not yet fully arrived:
Behold, days are coming," declares the LORD, "when I will make a new covenant with the house of Israel and with the house of Judah, not like the covenant which I made with their fathers in the day I took them by the hand to bring them out of the land of Egypt, My covenant which they broke, although I was a husband to them," declares the LORD. "But this is the covenant which I will make with the house of Israel after those days," declares the LORD, "I will put My law within them and on their heart I will write it; and I will be their God, and they shall be My people. They will not teach again, each man his neighbor and each man his brother, saying, 'Know the LORD,' for they will all know Me, from the least of them to the greatest of them," declares the LORD, for I will forgive their iniquity, and their sin I will remember no more." (Jeremiah 31:31-34)
Scripture describes the new covenant as having (at least) these elements:
- The Law written upon the heart
- Everyone will know God
- God will forgive the iniquity of Israel
Every believer today must recognize that not everybody knows God... therefore the new covenant hasn't fully arrived yet.
We also know that forgiveness of sin comes through faith in Messiah. As long as Israel as a nation has not accepted Yeshua (Jesus' Hebrew name) as the Messiah, God has not forgiven their sin. It is evident that believers today do not completely follow God's Law: we stumble, we struggle, and we strive against our sinful flesh.
Believers of today (both Jew and Gentile) are simply the "first fruits" of the promised harvest. We are a promise of the full harvest which is yet to come.
Second: The Law/Law of Moses/Sinai Covenant is not the "old covenant". The "old" covenant occurs when God's commandments are written on stone. The "new" is when God's commandments are written on our hearts (see above). I would completely agree that no believer is in the old covenant: the Law written on tablets of stone cannot do anything to change a person's spiritual state before God. Once God has taken us out of darkness and into His marvelous light (1 Peter 2:9), He begins the process of writing His Law upon our hearts... the promise of the new covenant!