Psalm 108 is an often-neglected psalm. Its first five verses are largely a repetition of Psalm 57:7-11, and verses 6-13 come from Psalm 60:5-12. To save space in long commentaries on the psalms, commentators frequently treat Psalm 108 briefly by saying, "See my comments on Psalm 57 and Psalm 60."
In a recent dissertation, Wyatt Graham takes a close look at Psalm 108, paying attention both to the slight changes the psalm makes in the material from Psalm 57 and Psalm 60, and to the placement of this psalm within the psalter. With regard to the placement of Psalm 108, Graham observes that Book IV of the psalter ends in Psalm 106:47 with a plea for restoration from exile. The at the beginning of Psalm 107, those redeemed from exile rejoice and give thanks to God (107:1-3).
Then Psalm 108 follows with David's confident prayer and statement of God's sovereignty, with a promise that God will again bring victory to his people in the future. After that come the imprecatory Psalm 109, which has traditionally been associated with the betrayal of the Messiah: and Psalm 110, which pictures the Messiah ascending to the right hand of God and serving as a priest like Melchizedek. Graham sees Psalm 108 contributing to the Psalm 108-110 trilogy., which looks forward to the coming of the Messiah to bring salvation and further restoration.
The superscriptions for Psalm 57 and Psalm 60 associate those psalms with particular times in David's life when God was with him. In Psalm 108, David seems to be looking ahead and anticipating future deliverance. We can see Psalm 108 fitting into the overall "story" being told by the psalter as a messianic prophecy.