Those who had been brought up under the old covenant, as a way of life, and who - subsequently - heard the gospel (which expresses the New Testament) were specifically warned not to turn back to the old covenant and were clearly warned of the dire consequences of doing so, by the writer of the epistle to the Hebrews.
We ought to give more earnest heed to the things which we have heard (Heb 2:1)
(says he - for he, also, heard these things from others and was not one of the original twelve who were with Jesus)
lest at any time we should let them slip.
He also says :
Take heed, brethren, (Heb 3:13)
(counting himself one with them)
lest there be in any of you an evil heart of unbelief in departing from the living God.
This departure is not to the ways of gentiles, to unmentionable sins and worldy luxuries, for what he is warning about is unbelief in the New Testament gospel. This departure from the living God is a potential departure from the new covenant back to an arrangement which merely foreshadowed the New Testament. But was not the reality.
Let us therefore fear, lest a promise being left of entering into rest, any of you should seem to come short of it
he says further, (Heb 4:1)
For unto us was the gospel preached as well as unto them.
The gospel was preached to the children of Israel as they engaged in an arrangement with God to display the coming New Testament in pictorial form - in artefact, in ritual, in sacrifice and in ordinance. But all of that was to be seen by faith. Not just to be ritually enacted, but to be understood. To be believed.
But the word preached .. (Heb 4:2)
(Note, 'preached'. The preaching was through demonstration. The word was expressed.)
did not profit them ... not being mixed with faith in them that heard.
They didn't actually believe it. They helped to enact it under an agreement with God (a covenant) but they never perceived the reality of it and never entered into it spiritually.
They needed to perceive that this - old - covenant was to be superseded. After which it would pass away and be but a memory. It was a picture. It was a demonstration. But what was to be believed was the reality.
Moreover that first covenant contained the law. It had to contain the law for mankind had put himself under law in Adam, choosing the tree of the knowledge of good and evil as a way of existing, favouring human understanding and human effort. (Rather than partaking of Life through receiving God's word.)
Thus the law was delivered - as part of the first covenant - at Sinai.
This do, and thou shalt live. (Luke 10:28)
But none ever 'did' the law. And none ever 'lived' through its ministration. It was a way of death, as forewarned in Eden.
In the day that thou eatest thereof ... thou shalt surely die. (Genesis 2:17)
So Paul also warns those who had heard the gospel from his lips, that after his departure they must, at all costs, reject those who would later come along and try to persuade them to mix old and new covenant. In this particular instance, the Galatian incident, it was an obligation to add circumcision to the gospel.
But it can be any of a variety of ways of mixing old and new.
Whichever method it is, is irrelevant for Jesus had already made it very clear that
new cloth unto an old garment .. the rent is made worse (Matthew 9:16)
new wine into old bottles ... the wine runneth out and the bottles perish.
One must - one must in the very nature of the covenants involved - thoroughly progress from the old to the new and, thereafter, fully appreciate that :
The law was a schoolmaster to bring to Christ. But after faith is come, we are no longer under a schoolmaster.(Galatians 3:24,25)
And Paul further warns them (of circumcision in this particular but it relates
to any kind of turning back to the old covenant) -
I, Paul, say unto you that if ye be circumcised - Christ shall profit you nothing.
So, in summary, and in specific answer to the OP :-
To cling to the old covenant ... is to lose Christ.
And he, alone, is salvation.
Neither is there salvation in any other: for there is none other name under heaven given among men, whereby we must be saved. (Acts 4:12)