The connection between Jesus Christ and the Sacred Scriptures of the Jewish people is not an immediate one, which is the way it has been reduced by the Jehovah's Witnesses and many literalist Christians.
For instance, there are no texts in any part of the Hebrew Scriptures (Old Testament) that speak of "the coming of the Messiah," especially in the sense advanced by Jehovah' Witness theology, namely that Jesus literally fulfilled the common expectation of the Jewish people in this regard.
In reality, not only does Judaism strongly hold that this is not true, the Roman Catholic Church (the largest and historically oldest of the Christian denominations) does not teach this idea either.
Recently the Pontifical Biblical Commission stated on this subject of the connection between the Old and New Testament regarding Christ as the link:
Christian faith [in the Catholic Church] recognises the fulfilment, in Christ, of the Scriptures and the hopes of Israel, but it does not understand this fulfilment as a literal one. Such a conception would be reductionist. In reality, in the mystery of Christ crucified and risen, fulfilment is brought about in a manner unforeseen. It includes transcendence. Jesus is not confined to playing an already fixed role — that of Messiah — but he confers, on the notions of Messiah and salvation, a fullness which could not have been imagined in advance....It would be wrong to consider the prophecies of the Old Testament as some kind of photographic anticipations of future events....The messiahship of Jesus has a meaning that is new and original.--The Jewish People and Their Sacred Scriptures in the Christian Bible.
The Jewish concept of "Messiah" is not directly found in Scripture but is, as most Jewish and Christian scholars now agree, post-Biblical or outside of the realms of Old Testament works. While there are indeed, and without reservation, prophecies about the Messianic age and messianic figures and the David dynasty being the ruling power in texts like those of the prophet Isaiah and even foreshadowed in some of the Psalms (and on this Jews definitely acknowledge), none of the same actually speak of "the Messiah."
As the document from the Pontifical Biblical Commission stated above, there are no texts that say "the Messiah will do such and such" or that "the Messiah will be this or that." The expression "the Messiah" never actually occurs in any of the Old Testament passages, even those that Jews consider to be Messianic prophecies. These texts often speak of a ruler, a king, usually "David," and speak of an era of peace, but never anything like "the Messiah will be a son of David" or "the Messiah will usher in the new world."
The expectations of the Messiah were quite limited by the time of the Second Temple era into which Jesus of Nazareth was born, and the idea was neither central to or universally accepted in Judaism. As the Catholic Church itself acknowledges, "Jesus is not confined to playing an already fixed role — that of Messiah — but he confers, on the notions of Messiah and salvation, a fullness which could not have been imagined in advance."
The Messiah concept of Jesus is far greater than anything imagined or even assumed necessary by the Jews. And the popular expectations of the Jews about the Messiah's role (i.e., that he would restore the Kingdom of Israel, liberate them from foreign rule, gather all members of the Diaspora back to the soil of Israel, usher in an era of enlightenment to all nations and the physical resurrection of the dead) never happened. Like the Catholic Church admits, Jesus cannot be the great Messiah of the New Testament and yet confined to the notions of Messiah held by the Jews or so lightly touched upon in Jewish Scripture. While there is a connection, it requires placing a new hermeneutic approach over the Jewish Scriptures, one which had not existed nor was ever available to the Jews before the Church standardized its doctrine about Jesus.
Thus the Jehovah's Witnesses and their concept of the connection between the two sets of Scriptures finds no support in Judaism or the oldest and original form of Christianity. To accept Jesus as Messiah and as "the connection between the Testaments" requires reading something new into the Scriptures of the Jews, at least according to Catholicism and Judaism.
