No, there isn't exactly a Psalm 151, or at least it's not titled such. But an additional one does occur in the
Greek Septuagint (LXX) translation of the Old Testament as a Psalm "outside the number," or a supernumerary Psalm,
about which I wrote two years ago. It is known especially in the Orthodox tradition, where it is accorded something close to canonical status. If Protestants are at all aware of it, they consider it part of the Apocrypha, those extra books (Judith, Tobit, the Maccabees, &c.) often included in an appendix after the New Testament or between the two testaments.
So I was surprised—pleasantly so, to be sure—to discover that our friends behind De Nieuwe Psalmberijming have recently posted a Dutch metrical versification of this psalm set to the Genevan tune for Psalm 19: Psalm 151. To be clear, the arrangement is not precisely of the version found in the LXX but of a longer version found at Qumran and thus part of the Dead Sea Scrolls. This psalm is unusual in being autobiographical in nature and is written in the voice of David himself. The story recounted is the familiar one in which David slays the Philistine warrior Goliath of Gath (1 Samuel 17).