When does the Old Covenant end and the New Covenant begin? We tend to forget that the Old Covenant does not end with Malachi and the New Covenant does not start with Matthew.
For the 33 years that Jesus walked the earth, He was still under the Old Covenant, which required following all its rules and regulations.
The New Covenant began when Jesus was crucified. When He said ‘It is finished’, He was talking about the Law, the Old Covenant. Upon His resurrection the New Covenant began and we are no longer required to try and live under the Law, and the way of the Old Covenant.
The old agreement was basically a tutor. A way God used to show humans that we were unable to live a perfect life on our own. It was a way to show us that we needed someone to save us from our sin. Once Jesus came and lived a perfect life on earth, He was able to be the sacrifice that fulfilled the Law and save each of us from our sinful nature (Matthew 5:17).
Now that the Law has been fulfilled in Christ, we are no longer required to try to live by the ten commandments, and the rules and regulations of the Old Covenant (Galatians 5:1-6). To many times we seem to forget that because of grace we now live by faith in Christ. We are no longer slaves to sin, we are no longer just a poor sinner saved by grace, although we were sinners and we are saved by grace. We are now the righteousness of God, through Christ. God no longer calls us slaves, but He calls us Sons (John 15:15). We are seated in heavenly places in Christ (Ephesians 2:6). This isn’t to say that we should go out and do what ever we want, right or wrong (Galatians 5:13). We do have freedom in Christ to do what we choose, but of course there are consequences if we choose things that God has warned us to stay away from.
Today we choose to live a life pleasing to God because of love (Matthew 22:37-40). Godly love is the fulfillment of the Law (Galatians 5:14, Romans 13:8 and 10, 1 John 3:23). We love God, we’ve been made righteous through Christ, and we are the temple of the Holy Spirit, who guides us, teaches us, and gives us strength. We do what is pleasing to God because we choose to out of love for Him, not out of obligation or because we are trying to fulfill a set of rules and Old Testament laws that we couldn’t live up to anyway.