It is known that Daawood (David) was sent as a Prophet after Moosaa (Moses), may Allaah exalt their mention, with a divine book. Then ‘Eesaa (Jesus), may Allaah exalt his mention, was sent with the Injeel (Gospel), which is a divine book as well. Why is it that the Jews held fast only to the book which was revealed to Moosaa (Moses), may Allaah exalt his mention, despite the fact that those mentioned books were revealed after it? May their book contain anything of the revelation that was sent to the Prophet Daawood (David), may Allaah exalt his mention?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His Slave and Messenger as well as that of his family and all his companions.

Allaah, the Exalted, made it a condition on the people to believe in all the Books that were revealed to all the Prophets, may Allaah exalt their mention, and clarified that believing in some of them while disbelieving in others, is an act of disbelief which necessitates a severe and painful torture. Allaah Says (what means): {Say, [O believers], “We have believed in Allaah and what has been revealed to us and what has been revealed to Ibraaheem (Abraham) and Iamaa’eel (Ishmael) and Ishaaq (Isaac) and Ya’qoob (Jacob) and the Descendants [Al-Asbaat] and what was given to Moosaa (Moses) and ‘Eesaa (Jesus) and what was given to the prophets from their Lord. We make no distinction between any of them, and we are Muslims [in submission] to Him.”}[Quran 2:136]. Allaah further Says (what means): {Indeed, those who disbelieve in Allaah and His Messengers and wish to discriminate between Allaah and His Messengers and say, “We believe in some and disbelieve in others,” and wish to adopt a way in between. Those are the disbelievers, truly. And We have prepared for the disbelievers a humiliating punishment.}[Quran 4:150-151].

As regards your question about the Jews, why they held fast only to the book which was revealed to Moosaa (Moses) and did not stick to other revelation, then this is among their aberrant deviations. What is worse is that they did not even stick to the book which was revealed to Moosaa (Moses) ; they believed in some texts of it and disbelieved in some other texts of it, and concealed the truth, and falsified some of it.

With regard other Prophets, may Allaah exalt their mention, who were sent to them, the Quran stated that they used to follow their desires in dealing with them. Allaah Says (what means): {Whenever there came to them a Messenger with what their souls did not desire, a party [of Messengers] they denied, and another party they killed.}[Quran 5:70]. As regards your question whether their book contained anything of the revelation that was sent to the Prophet Daawood (David) this is something possible but this could not be authenticated by the books which they have in their possession at the present time as they falsified them and forged them, and mixed the truth with falsehood. It is for this reason that we are not permitted to believe in what they say except in what our religion proved to be the truth.  

Allaah Knows best