An analogy for the Old Testament and New Testament can be this: The Old Testament is like the radio and the New Testament is like the television.
That can give us an idea of the connection between the Old Testament and the New Testament.
In the Old Testament, the Word of God came upon priests, prophets and kings, and they proclaimed what they had heard from God.
They may not have "seen" the face of God but they know His voice.
In the New Testament, the Word of God became man in the person of Jesus, and people saw God in Jesus.
Jesus brought about a new covenant between God and mankind. The old covenant "disappeared" with the establishment of the new convent.
But just as radio sets have given way to television and computer sets, the transmission over air waves is still needed as in the case of wi-fi or wireless transmission, and even developed further.
With Jesus establishing the new covenant between God and man, what has essentially remained of the old covenant is the relationship between God and His people, a relationship that was brought to a deeper level by Jesus on the Cross.
Even at the individual level, the covenant between God and us must be renewed everyday through prayer and penance. Without daily prayer and penance, the covenantal relationship between God and us will disappear and might be gone forever.