The Bible is more than two covenants Old and New. There are multiple covenants in the Old Testament. There are the Adamic, Noahide, Abrahamic, Sinaitic, and Davidic Covenants. Two of them axis in the tie frame of the New Testament.
The Adamic covenant is simply the foundation of creation and involved a curse of death if broken. Then the Noahide Covenant starts with Noah in any rules given when he came off the ark apply to all Gentile nations. Then Abraham has a unique covenant for him and his descendants, that requires circumcision. Then the Sinaitic Covenant is an extension of the Abrahamic Covenant because it is for his descendants that will enter the promised land, this is what Moses set up for them on Mt. Sinai. You can think of this as a marriage, with Abraham’s covenant being the engagement, and the Sinai agreement being the wedding. God also made a covenant with David, which is similar to the Abrahamic covenant since it affects one bloodline and proclaims that the Messiah will come from his lineage.
The exile is sort of a temporal divorce (Jer 3:8 uses the words of a Jewish divorce certificate) and that represents a temporal fracture in the Sinaitic Covenant. In Hosea chapters 1-3, God has Hosea marry a prostitute named Gomer, and she cheats by prostituting herself, then another man pimps her out. Divorcing her is his legal right because of her adultery, however, God tells him to buy her back from her lover and reconcile with her. This ends up becoming a metaphor for what God will do with Israel after the exile, despite their idolatry. The Israelites are restored 70 years later however God’s presence is not in the most holy place of the 2nd Temple. So they are essentially on probation until the Messiah appears then he will remarry them along with gentile believers. God’s presence returned in Acts chapter 2, after Jesus’ ascension, to make the human bodies of believers in christ his new Temple.
In addition, the New Testament writings transition between two covenants. The gospels are still under the old Sinaitic covenant because Jesus had not risen yet and there is no Holy Spirit distribution. After the resurrection was the beginning of the new covenant and Acts chapter 2 is the beginning of the church movement initiated by the distribution of the Holy Spirit on Shavuot (Pentecost). The marriage covenant analogy I made earlier also applies to the New Covenant as well, because Jesus’ resurrection and the Holy Spirit distribution represent the engagement but the wedding is when he returns to retrieve his bride, which is the body of Christ (the church).
The Adamic covenant (or framework) is in action at the time before Noah and was based on God’s covenant with Adam and Eve that was broken by their sin, causing the fall of creation. Under this Covenant, things like murder and such were sins but they weren’t punished by God since he gave Cain mercy through the mark. However, Cain’s descendant Lamach took that mercy out of context, treated it like a reward, and came up with the idea that when you murder someone you’ll get a bonus of protection. I call this the “Murder Olympics” as we can see in Gen 6:11. God was grieved by this foolishness so he had to execute judgment, but at the same time preserve humanity in order to fulfill his promise to Adam and Eve to save humanity from this sinful state.
God punished that world with the flood and spared Noah because he was the best of them and made a new covenant marked by the rainbow, this is the Noahide Covenant. This covenant applies to all people Jews and Gentiles and is where the moral laws take more direct effect with specific punishments. For example, the death penalty was introduced for the first time for murder in Genesis 9:5. For people who have objections to the death penalty, and don’t understand why a loving God would cause such a thing, all they have to do is read Genesis chapters 4-9 and they’ll see that when he didn’t give the death penalty for murder, there was mass violence, so it was necessary to stop people from doing that again. In Genesis 9 we are also introduced to meat-eating and there is no dietary restriction on clean versus unclean meats, although clean vs unclean animals are distinguished when Noah put them on the ark (7 pairs of clean land animals and flying creatures, and one pair of each kind of unclean land animals). The only catch is to avoid drinking blood and this is forbidden in the Sinaitic Covenant (Lev 19:26, Deut 12:16-25) and even in the Messianic Covenant in Acts 15:19-21.
The only requirement in the Abrahamic Covenant is for Abraham’s descendants to worship God (YHWH) and to circumcise the boys on their eighth day. This covenant offers a blessing to all of Abraham’s descendants, for God said He would “bless those who blessed Abraham and curse those who curse him” (Gen 12:1-3). Abrahams’s descendants include Ishmael from his concubine Hagar, Isaac from his wife Sarah, and from his 2nd wife Keturah (whom he married after Sarah died) he has Zimran, Jokshan, Medan, Midian, Ishbak, and Shuah. Isaac however has a special blessing because his mother was Abraham’s first wife and received a special place in the Abrahamic covenant. Like Abraham she also had her name changed in Genesis 17. Even though Ishmael was the firstborn God said that Isaac would be the promised seed (Gen 17:15-22). This covenant was offered at a time when Abraham had no children and God promised to give him an heir through his wife Sarah. Unfortunately, Abraham and Sarah tried to make things happen on their own through Hagar which produced Ishmael and strife between Sarah and Hagar, which later spills over into Ishmael and Isaac. Abraham and Sarah’s lack of faith lead to the abuse of Hagar and this was not the promised seed that God would supernaturally impart to them through Sarah’s womb. Isaac however was Sarah’s only child and therefore the child of the promise.
The Sinaitic Covenant is the Covenant established on Mount Sinai with Moses (Ex ch. 20). The laws introduced here are often called the Mosaic Law. The Sinaitic Covenant includes the moral laws from the Noahide (like the ones against murder and adultery) and the circumcision law from Abraham. In addition, there are new laws introduced that specifically apply to the Israelites. Some of them only apply immediately, like not making false gods and idols, while others only apply after they’ve conquered the promised land, like rules government land allotments, slavery, tithes, offerings, etc. These laws teach the Israelites ritual and moral purity for living in God’s presence and representing him on earth as a nation of priests (Ex 19:6) to the Gentiles. There was a blessing of expansion and longevity for keeping the law, but a curse of destruction and exile for breaking it (Deut ch, 7, 9, 28). God had them build a special tent called the Tabernacle where his presence would dwell and he set the Levites apart for helping the priest serve in God’s presence by managing the sacrifices and ritual purification ceremonies, as well as functioning as stewards of the law who teach the common people. The rest of the Israelites would get tribal land allotments and were required to share 10% of their harvest with the Levites because they didn’t have a land allotment. Some moral laws were punished by restitution or debt enslavement, but other more serious crimes were punished by execution but required at least 2-3 witnesses in order to execute death. Their goal was to preserve God’s ways and laws until the Messiah came but they failed and got exiled. However, God restored them and abided with them in silence until the Messiah came and offered the new Messianic covenant through Jesus.
In 2 Sam 7, God made the Davidic covenant with David which says that if his descendants remain faithful that he will be a blessing to them. In this Covenant, he also confirms that David’s lineage will lead to a greater King, the Messiah himself. However, Solomon sinned and that Covenant was broken by their descendants. Despite this God remained faithful to his Covenant to David in the Messiah would still come through his lineage just not from Solomon’s line. Look at Luke 3:23-38 for more details on the biological lineage of Jesus to David through Mary. Jesus was blood-related to David through Solomon’s younger brother Nathan.
The Messianic Covenant initialed by Jesus the Messiah connects Jews and Gentiles into one Covenant. The Sinaitic did not go away but was simply fulfilled in specific ways. The ritual purity laws, the priestly system, the sacrificial system, and the holy days are fulfilled in Jesus in one way or another. It is only the moral laws we follow until we get the new bodies that will be sin-free, and it is the job of the Holy Spirit to help believers in the messianic covenant follow those moral laws. In addition, because Christ died in our place, we no longer have experienced the death penalty under the Sinaitic covenant, but there is eternal condemnation executed on judgment day for those who reject the messianic covenant (John 3:16-21).
Hebrews chapters 5-7 are about Jesus’ role as our new covenant High Priest in the order of Melchizedek. Hebrews 8-10 says that Jesus is the greatest sacrifice that cleanses us of sin rather than just covering like the animal sacrifices in the law did. Jesus is the ultimate sacrifice, and scapegoat (like the Yom Kippur scapegoat) because he took our sins on himself. Jesus is our priest who poured out his blood on the altar in heaven (Heb ch. 9). Furthermore, we don’t need to be in a clean state (ritually pure) to interact with God’s presence anymore. This is because he no longer resides in a Temple/Tabernacle, believers are “living temples” now. According to the NT, believers have God’s spirit inside of them because they were made pure by the sacrifice of Jesus, making their bodies new Temples rather than having to build another one in Israel (1 Cor 6:19-20, & 2 Cor 6:15-18). Also, Jesus’s blood has made sanctified people as if they were washed with “pure water” (Heb 10:22). Ritual impurity was solved by taking a bath in the old testament, so Hebrews 10:22 is saying Christ’s blood functions like water in that sense and solves all ritual impurity. In the Old, Testament humans could not go into God’s presence if they were ritually impure. Ritually impure people were people who recently touched an unclean animal carcass, a dead human, were menstruating or touched by menstrual blood, had bodily discharges or skin diseases, or touched someone that had these issues, or had recently had sex. God’s spirit is now dwelling inside believers so that is a sign that something has changed in our status. Jesus who was filled with the holy spirit was able to heal lepers and people’s bodily discharges by touching them without becoming ritually impure himself, so believers who follow Jesus can do the same since they to have the same spirit (Romans 6:10-11).
HOWEVER, Gentile in the messianic covenant, like Jews, are still required to follow the Moral purity laws (Lev18-20). Moral purity laws still apply because we have sin nature and we are waiting on the new bodies to be free from that (1 Cor 15:35-58, 2 Cor 5:1-10, Phil 3:20-21). The holy spirit is here to aid us in overcoming sin nature and following the moral laws (John 14:15-18). Only those that receive Jesus’s covenant will have access to the holy spirit (Rom 8:5-11). Believers overcome sin by following the holy spirit’s instructions instead of their fleshly desires (Gal 5:16). If we sow into the flesh we reap corruption, if we so into the spirit we reap eternal life (Gal 6:7-8). The moral purity laws are referenced in the new testament in Acts 15:22-28 when the Jerusalem council determined that Gentiles followers of Jesus didn’t ritual purity laws but did need moral laws.