The Old Testament (Covenant) is understood by most to be a collection of books (Genesis - Malachi), and the New Testament is understood to be a collection of books (Matthew - Revelation).
However, this is an incorrect understanding.
The Old and New Testaments (Covenant) are not a collection of books but each testament reveals how God relates to people at different times in history.
The OT communicates how God related to Israel under the Law of Moses (Book of the Law, Book of Moses, or Written Code - Exodus 19-Leviticus, Deuteronomy) and the New Covenant is how God relates to everyone who receives his grace through faith in Jesus.
The OT (covenant) was a conditional (if, then) testament where blessings where based upon Israel's obedience to the law - which the people NEVER obeyed (Ten Commandments and all the other laws) and forgiveness for breaking the law was temporarily given through the animal sacrificial system.
The OT was a testament of condemnation and death, was temporal, and has no glory compared to the new covenant of grace (2 Corinthians 3:4-11).
Contained in the OT was God's promise to replace the OT of Law with the New Testament of Grace (covenant) (Jeremiah 31:31-34).
In the NT, God remembers our sins no more because Jesus died for all of our sins (Hebrews 8:12, 10:17-18).
In the NT, God doesn't count our sins against us because all of our sins were counted against Jesus (2 Corinthians 5:19).
In the NT, forgivenss is complete and eternal (Hebrews 8-10). In the NT, we have eternal life and are declared righteous (innocent, not guilty of breaking the 10 Commandments) by God (2 Corinthians 3:9, 5:21).
In the OT, God promised to send his Spirt into the hearts of people so they could live and love (Deuteronomy 30:6).
In the NT, God redeems people from the law through Jesus and sends the Spirit of Jesus into our hearts where we call God Abba, Father and where the Spirit produces love in and through us (Romans 5:5, 7:6, 8:15-17; Galatains 4:4-6, 5:23-23).
In the OT, God is a judge under law, even though all he ever wanted to be was Father (Jeremiah 3:19).
The New Tesament (Covenant) of Grace replaced the Old Covenant (Testament) of Law (Hebrews 7:22, and Hebrews 8, 10).
The Old Testament went into effect with the blood of an animal (Hebrews 9:18-22; Exodus 24:6-8).
The New Testament went into effect with the blood of Jesus (Matthew 26:28; Luke 22:20; Hebrews 9:24-10;18).
The New Testament is everything Jesus did for us to reconcile us to God (2 Corinthians 5;19-21).
We learn about this in Paul's letters such as Romans, Galatians, Ephesians, 2 Corinthians 3:1-6:2, Philippians, Hebrews, and Colossians.
If you are in Christ, you are a new creation. The old covenant of law is gone and the new covenant of grace has come (2 Corinthians 5:17).
You are free now...no longer living under the condemation of the law but living under the freedom of grace by the Spirit of Jesus who lives in you (2 Corinthians 3:18).