Most people think the dividing line between Old and New Testament is when the Gospels start in chapter One. Jesus was born under the Law (Old Covenant) and kept it perfectly without fail even in the slightest way. The New Covenant did not start until after the Cross where Jesus finished the work He came to accomplish. When He said, "It is finished!", the veil in the Temple that separated God from man was torn in two. Mankind who was separated from God because of the Law of Moses was now able to approach God through Faith. Because of Faith, God's Grace is manifested in our lives.
The main clause of the New Covenant is found in Hebrews 8:12 which says, "I will be merciful to their unrighteousness & their sins and lawless deeds I will remember no more." What Mankind lost in the fall when Adam sinned, (complete fellowship with God) was restored when Jesus (the 2nd Adam) rose from the dead and then gave us the Holy Spirit (God indwelling in us). This is indeed the "Good News" of the gospel.
Paraphrased from Joseph Prince's book 'Destined to Reign'