And beginning with Moses and all the Prophets, he interpreted to them in all the Scriptures the things concerning himself.
An approach that I take when reading Scripture rests on verses like this one. Yes, there is an Old and New Testament, but there is one Bible. One Bible that reveals to us who God is, and that revelation is seen most clearly in Jesus Christ. It is not only permissible for us to read sections of the Bible that are not explicitly about Jesus and to see him there, but it is necessary to fully understanding Scripture.
In Luke 24, Jesus is on the road with two men who do not understand that Jesus had to die to fulfill God’s Word. They say, “We had hoped that he was the one to redeem Israel.” They had hoped. But because they did not understand Scripture they in turn do not understand Jesus and what he came to do. Jesus says they are foolish and are slow to believe all the prophets spoke because the prophets spoke of himself.
Jesus Christ is the center of our faith and he is revealed throughout all of Scripture.