The relationship between Jesus and the Old Testament was an important matter for the early Church, especially the early Jewish Christians.
St Peter deals with the question in his first letter. He says that the prophets carefully searched out and examined the meaning of salvation. We might put it slightly differently: the Prophets in a special way meditated on the meaning of God's promise of a Messiah and how God was working towards the fulfilment of that promise all through the history of Israel and the life of the Chosen people. The prophets kept the promise and the hope of salvation alive in the religious life of Israel, especially in times of great disaster.
Peter then adds for his early Christian readers, and for us: "They prophesied the divine favour that was to be yours." All of the Old Testament in different ways points to the mystery of salvation through the Messiah, whom we now accept as our Lord and Saviour Jesus Christ.
Attention to the ways in which God worked through history to fulfil the promise of a Messiah teaches us to be attentive to God working in our own lives to help us understand and accept the gift of salvation.
Father, by the grace of Baptism may we more consciously accept and enjoy the gift of salvation.