The correct answer the original question is as follows:
Short version: the only thing that makes the covenant new is that there is no longer any animal sacrifices to atone for sins, but faith that the messiah forgives your sins. The word paul uses for "new" is kainos(strongs 2537), which means new, as in refreshed, not brand new. Neos means brand new. We are under a refreshed covenant not a brand new one. Paul uses kainos for a reason.
Explanation: there are 3 parts of the law- commandments, statutes, and ordinances. Paul is almost always referring to the the "ordinances" of the law...i.e. "The sacrificial system" (the works of the law), which were later added to the previous commandments and statues, through moses.
The commandments and statutes were way before moses. Even abraham followed them (Genesis 26:5), as well as Isaac, and then Jacob, before he and the whole family moved into Goshen (Genesis 46:28-29, 47:1). There was no tabernacle/temple sacrificial system when they (the hebrews) went into Egypt. The sacrificial system was added 430 years later, after coming out of Egypt, because they had been breaking the previously established commandments and statutes and needed an atonement for their sins. That's one reason Yahweh gave it to them.
Yahweh said "the soul that sins, it shall die" - Ezekiel 18:20. However, these "ordinances/animal-blood sacrifices" given by Yahweh postponed the death penalty (just as it did for Adam and Eve when Yahweh killed an animal for them). The added sacrificial system was also a way to prepare the minds of those coming out of Egypt, for the idea of the spilling of innocent blood being able to atone for the breaking of the previously established commandments & statutes (given and followed before Moses)...sin - I John 3:4.
The sacrificial system was the tutor/the schoolmaster/the thing that pointed to the messiah! The messiah's innocent blood was spilled, and he died as the final sacrificial lamb. Because of this, "the bond written in ordinances" was blotted out- Colossians 2:14. Notice Paul didn't say commandments or statutes...only ordinances. At the time, the temple was still standing and the sacrifices were still being done. That's why Hebrews 8:13 says: 'in that he says, a new (kainos) covenant, he has made the first old. Now that which decays and grows old is ready to vanish away." The new covenant is signified by the vanishing of the temple animal sacrificial laws...not the rest of the laws (commandments and statutes).
This is why people are in error about Paul saying: "we are not being under the law, but under grace". Paul was only ever talking about the sacrificial law not the rest. That confusion happened during his time as well, and to this very day Paul is still being interpreted wrong...read Acts 21:21-24 - "they are under the impression that you teach all the Jews who live among the gentiles to forsake the law of Moses, telling them not to circumcise their children or observe our jewish customs. What should we do? They will certainly hear that you have come. Here's what we want you to do. We have four men here who have completed their vow (Numbers 6). Go with them to the temple and join them in the purification ceremony, paying for them to have their heads ritually shaved. Then everyone will know that the rumors are all false, and that you yourself observe the jewish laws."
If you don't know the Old Testament laws, you will not easily understand Paul...(II Peter 3:16). He was writing to people whom he had been commissioned to talk to in person, about following the law of moses (Acts 15:20). Therefore they knew what he meant in his letters when he used the term "the law"...meaning the sacrificial laws/ordinances...(Though sometimes circumcision as in Galatians).
There are no more animal sacrifices and no more temple. We must now have faith in the messiah Yahshua that our unintentional sins are forgiven. This is when we "mistakenly" overstep the boundaries of the commandments and statutes...not when on purpose. Sin is "the transgression of the law (commandments & statutes)...(I John 3:4). However, if you can read your bible, learn the commandments and statutes, but still break them, "there remains no more sacrifice for sin..."(Hebrews 10:26). If you love him, you will keep his commandments...(I John 5:3). If you are "of Yahweh" and not the devil, you will not break them...(I John 3:8-9). The commandments & statutes are in the Old Testament...(I John 2:7). We must love one another, "but" we are only loving one another biblically (not humanly/emotionally), if we follow his commandments/the law. Shalom.