The book of Psalms is actually one of the later products of the Old Testament era. If we were to arrange the books of the Old Testament according to their dates of compilation, we would have to put the Psalter among the post-exilic volumes toward the very end of the collection. Many of the songs contained in it are, to be sure, much older, but the particular selection and arrangement of Hebrew hymns into the volume we call the book of Psalms is a post-exilic work. In fact, rather than looking at the Psalter as an Old Testament worship hymnal, it is probably more appropriate to regard it as a final product of the Old Testament temple, compiled in preparation for New Testament worship.
Sing a New Song: Recovering Psalm Singing for the Twenty-First Century, Loc. 2020.