Old Covenant, New Covenant
God made a covenant with Israel in the wilderness.
Jeremiah 31:31 "Behold, days are coming,” declares the Lord, “when I will make a new covenant with the house of Israel and the house of Judah." Hebrews 8:13:
"When He said, 'A new covenant,' He has made the first obsolete. But whatever is becoming obsolete and growing old is about to disappear."
The NT writers see the fulfillment of the new covenant prophecy in the new order inaugurated by the work of Christ. He said in 1 Corinthians 11:25: "In the same way He also took the cup after supper, saying, 'This cup is the new covenant in My blood; do this, as often as you drink it, in remembrance of Me.'”
The word testament originally meant covenant, so each Testament is divided by which covenant it is related to.
(The Origin of the Bible: Newly Updated by F. F. Bruce, J. I. Packer, Philip W. Comfort, and Carl F. H. Henry, 2020. Page 5.)
Other Covenants in the Bible
Noah's Covenant
God blessed Noah and his sons, saying to be fruitful and multiply and that the fear of them shall be upon every beast, bird, and fish. Every moving thing shall be food for them, but they shall not eat flesh with its blood. For their lifeblood, God will require a reckoning, be it from beast or man.
God also established his covenant with Noah and his offspring, as well as with every living thing from the ark. "I establish my covenant with you, that never again shall all flesh be cut off by the waters of the flood, and never again shall there be a flood to destroy the earth.”
And God said, “This is the sign of the covenant that I make between me and you and every living creature that is with you, for all future generations: I have set my bow in the cloud, and it shall be a sign of the covenant between me and the earth. When I bring clouds over the earth and the bow is seen in the clouds, I will remember my covenant that is between me and you and every living creature of all flesh. And the waters shall never again become a flood to destroy all flesh. When the bow is in the clouds, I will see it and remember the everlasting covenant between God and every living creature of all flesh that is on the earth.” God said to Noah, “This is the sign of the covenant that I have established between me and all flesh that is on the earth.”
(Genesis 9)
Abrahamic Covenant
The Lord said to Abram, "Go from your country and your kindred and your father's house to the land that I will show you. I will bless those who bless you, and him who dishonors you I will curse, and in you all the families of the earth shall be blessed.” When Abram came through Canaan to Shechem, to the oak of Moreh, the Lord appeared to Abram and said, "To your offspring I will give this land." On his journey, Abram built two altars to the Lord. (Genesis 12:1-9)
Jonathan & David
Jonathan brought David into a covenant of the LORD. (1 Samuel 20:8)
Jonathan made a covenant with the house of David, saying, "May the LORD take vengeance on David's enemies" (1 Samuel 20:16)
Davidic Covenant
David told Nathan his thoughts about building the Ark a house, and the LORD responds through Nathan that David is not called to build the LORD a house. But the LORD is going to build David a house. An offspring from his body will build a house for His name, and He will establish the throne of His kingdom forever. His steadfast love will not leave him. David's house and kingdom shall be made sure forever before Him. (2 Samuel 7) Jesus is the root and the descendant of David. (Revelation 22:16)
Hosea Covenant
And in that day, declares the Lord, you will call me 'My Husband,' and no longer will you call me 'My Baal.' For I will remove the names of the Baals from her mouth, and they shall be remembered by name no more. And I will make for them a covenant on that day with the beasts of the field, the birds of the heavens, and the creeping things of the ground. And I will abolish the bow, the sword, and war from the land, and I will make you lie down in safety. And I will betroth you to me forever. I will betroth you to me in righteousness and in justice, in steadfast love and in mercy. I will betroth you to me in faithfulness. And you shall know the Lord.
And in that day, I will answer, declares the Lord, I will answer the heavens, and they shall answer the earth, and the earth shall answer the grain, the wine, and the oil, and they shall answer Jezreel, and I will sow her for myself in the land. And I will have mercy on No Mercy, and I will say to Not My People, 'You are my people'; and he shall say, 'You are my God.'
Secular Covenants
Deuteronomy and the Pentateuch as a whole resembles a 2nd millennium B.C suzerainty treaty, which forms a covenant between a suzernation and his subjugated neighbor.
(The Origin of the Bible: Newly Updated by F. F. Bruce, J. I. Packer, Philip W. Comfort, and Carl F. H. Henry, 2020. Literature in Bible Times by Milton C. Fisher, Page 99-100.)