The Quran mentions previous scriptures and regards itself as a continuation in this line of revelation. It is the final and ultimate guard/criterion over previous scripture:

And We sent in their footsteps Jesus, son of Mary, authenticating what was present with him of the Torah. And We gave him the Injeel/Gospel, in it is a guidance and a light and authenticating what was present with him of the Torah, and a guidance and an admonition for the righteous.
And let the people of the Injeel/Gospel judge with what God has sent down in it. And whoever does not judge with what God has sent down, then these are the wicked.
And We have sent down to you the decree with the truth, authenticating what is between your hands of the decree and as a guardian/superintendent over it. So judge between them by what God has sent down, and do not follow their desires, when has come to you of the truth. For each of you We have made a law and an open way; and if God had willed, He would have made you all one nation, but He tests you with what He has given you; so strive to do good. To God you will return all of you, and He will inform you regarding that in which you dispute.
[5:46-48]

It states that SOME of the followers of previous revelations became misguided due to distorting/adding parts to what was revealed to them [2:75, 2:79], and following some parts and not others [2:78, 5:15, 5:43-44].
For example the doctrine of Trinity is not explicitly taught in The Bible and is a later addition, please see the following entry (and research 'Comma Johanneum'): https://www.britannica.com/topic/Trinity-Christianity

However, The Quran clearly states that some remained true to the original message in the previous scriptures and they still contain truth [3:113-115, 5:43, 5:65-66, 32:23]. For example, it speaks about what was given to Moses in a positive light:

But when the truth came to them from Us, they said: "If only he (the messenger) was given the same that was given to Moses!" Had they not rejected what was given to Moses before? They had said: "Two magicians assisting one another." And they said: "We reject all these things."
Say: "Then bring forth a decree/book from God that is better than both of them* in guidance so I may follow it, if you are truthful."
[28:48-49]
*i.e. the scriptures given to prophet Moses and prophet Muhammad

Summary: A recurrent theme in The Quran is that the human being is oft forgetful, thus periodic reminders (e.g. Torah/tawrat, Gospels/injeel, Psalms/zaboor, Quran) are sent to reaffirm the covenant with God. This gives us a pluralistic/inclusive perspective in which to view all revelations from God - every scripture revealed to mankind on earth is ultimately a recognition, renewal, and continuation of this relationship.

READ - click to look up verse references