There is no <Old Covenant> of God as there is no old sabbath of the LORD.
Actually there is, and it is recorded in a collection of books called the "Old Testament." The first five books of that collection are the "books of Moses" that contain the covenant God made with the nation of Israel when he delivered them from the bondage of Egypt a very long time ago, a covenant based on the Law given through Moses, a very long time ago. That first covenant that is recorded in the first testament included the commandments concerning the Sabbaths and their observances and all their sacrifices and offerings and ordinances, as well as prophesies about what the Sabbaths foreshadowed.
But through Jeremiah (31:31-34) God foretold that the day would come when he would make a "new covenant." Now Paul says in Hebrews (8:6-13) that the new covenant mediated by Jesus is better than that first covenant, and being a new covenant means the first covenant had grown old and at the time of Paul's writing the letter to the Hebrew Christians that first covenant, the Mosaic Covenant, having grown old (some 1400 years old in fact), was ready to vanish away.
So it is not only Biblically sound but is imminently acceptable to speak of the two covenants as the "Old" and the "New."
To speak of an old covenant sabbath is to speak ineffable nonsense, and to speak of a sabbath day as God’s Rest is unspeakable blasphemy.
Careful there my friend, else you find yourself calling the Apostle Paul and even God himself blasphemers.
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For [God] spake in a certain place
of the seventh day on this wise, And God did rest the seventh day from all his works. And in this place again, If they shall enter into
my rest." That "certain place" Paul mentions where God said these things about the 7th day and about God's people entering
his rest is through David. Read this and think on it very carefully:
"To day if you will hear his voice, Harden not your heart, as in the day of provocation, and as in the day of temptation in the wilderness: When your fathers tempted me, proved me, and saw my work. Forty years long was I grieved with this generation, and said, It is a people that do err in their heart, and they have not known my ways: Unto whom I sware in my wrath that
they shall not enter into my rest." (Psalms 95:7-11)
Paul cites this word from God to explain that there is a rest that the 7th day foreshadowed, what Isaiah beautifully calls "the resting place:" Again, read it carefully and prayerfully:
"For with stammering lips and another tongue will he speak to this people. To whom he said,
This is the rest wherewith ye may cause the weary to rest; and this is the refreshing; yet they would not hear. But the word of the Lord was unto them precept upon precept, precept upon precept; line upon line, line upon line; here a little, and there a little; that they might go and backslide, and be broken, and snared, and taken." (Isaiah 28:9-13)
So if you are laboring under the misguided notion that the "rest" of God is limited to only the 7th day Sabbath, you should consider that it doesn't require "faith" to take Saturday's off work. But it did require faith for the Israelites to cease their wanderings and enter the promised land (the resting place), which they failed to do
because of unbelief.
"Seeing therefore it remaineth that some must enter therein, and they to whom it was first preached entered not in because of unbelief: Again, he limited a certain day, saying in David, "To day, after so long a time; as it is written, To day if ye will hear his voice, harden not your hearts, For if Jesus had given them rest (the Israelites kept the 7th day Sabbath during the wilderness wanderings), then would he not afterward have spoken of another day. There remaineth therefore a rest to the people of God. For he that is entered into his rest, he also hath ceased from his own works, as God did from his. Let us therefore labor to enter into that rest, lest any man fall after the same example of unbelief." Hebrews 4:6-11
The weekly Sabbath, like everything else in the Law, was temporary, no matter how meticulously it was observed one had to get up the next day and go back to work. So by it's very nature it was a temporary rest, just as by it's very nature the Old Covenant atonement for sin was temporary and had to be repeated year after year. But the Sabbath, indeed all the sabbaths served as a shadow of a day that God had ordained when His people would find and enter into that place of God's rest and never again have to labor for their daily bread and meat.
There's an old hymn that I think says all this far more beautifully than I can:
My faith has found a resting place
Not in device or creed
I trust the Ever-Living One
His wounds for me shall plead
I need no other argument
I need no other plea
It is enough that Jesus died
And that he died for me.
In Christ,
Pilgrimer