Seems that you are ignoring the fact that the 10 Commandments ARE the Old Covenant. And that being the case, are you suggesting that Christians are not really under a new covenant, but under the Old? (Of course, you would not be the first to do this).
Are you saying that the 10 commandments are no longer to be kept?
Since the OC is not made obsolete but is made BETTER, we all are still also under the OC since we gentiles have been grafted in.
Romans 11
The NC is a far better covenant and is completed, or fulfilled, in Christ.
The 10 commandments are still in force.
Stealing was a sin 3,000 years ago and it's a sin today.
The atheist world lives by the 10 commandments.
The NC is a better covenant because it required only ONE sacrifice forever more.
Leviticus 17:11
The life is in the blood.
And God has given us HIS blood to atone for our sins.
This does not mean there are no more sins which require forgiveness.
Sin still exists because we break the 10 commandments but we have an advocate to speak for us with God Father and no further sacrifices are necessary.
Hebrews 9:22
We are made FREE TO OBEY God and to live for HIM.
We are made free to flee from acts that lead to death.
Sin STILL equals death.
By our belief in Jesus, that is a free gift from God through our faith in Him, Jesus has made it possible for us to have a right relationship with God and to serve him freely and happily because of mutual love.
The 10 commandments have not been abolished.
They are still in effect.
Jesus quoted each one of them.
This would require some study, but we could do this if you wish.
Also, remember that Jesus said to the adulterous woman:
"Go and sin no more".
Jesus expects us to keep the commandments.