Five psalms in the Psalter are called “new songs” (Pss. 33:3; 40:3; 96:1; 98:1; 149:1). Additionally, while Psalm 144 is not itself a “new song,” it includes a promise to sing a “new song” (v. 9) after God grants a longed-for victory. In biblical Hebrew, a new song is not necessarily a song that was recently written. The phrase is an idiom for a certain kind of praise song—the kind of praise one sings loudly for all the nations to hear after God has granted a great victory. Psalm 40 is a good example: “I waited patiently for the LORD; and he inclined unto me, and heard my cry. He brought me up also out of an horrible pit, out of the miry clay, and set my feet upon a rock, and established my goings. And he hath put a new song in my mouth, even praise unto our God: many shall see it, and fear, and shall trust in the LORD” (vv. 1–3, emphasis added).

Joel R. Beeke, Anthony Selvaggio, Sing a New Song: Recovering Psalm Singing for the Twenty-First Century, Loc. 83