The traditional Hebrew Bible and the Christian Bible contain 150 psalms. However, some versions of the Bible, such as the one used by the Greek Orthodox Church, contain Psalm 151.
Psalm 151 is not considered canonical in either Protestantism or Catholicism and is not included in most Protestant or Catholic Bible translations. The psalm purports to have been written by David and speaks of his selection by God as the new king of Israel and of David’s victory over the Philistine giant, Goliath. Psalm 151 is quite autobiographical, giving details of David’s life such as his flute-playing and harp-making; his anointing by Samuel, who bypassed his brothers, “handsome in form and appearance: / Their stature tall, / their hair beautiful” (Psalm 151:5–6, CEV); and his beheading of Goliath.
Until the twentieth century, Psalm 151 was only known to modern scholars as a Greek, Latin, or Syriac text, appearing in the Septuagint and translations made from the Septuagint. But then the Dead Sea Scrolls were discovered, and Psalm 151 was found in one of the scrolls. The Hebrew version of Psalm 151 (in the Qumran scrolls) differs somewhat from the LXX translation; in the Hebrew version, the psalm is split into two separate texts, which are then combined and condensed into a shorter text in the LXX.
There are a couple reasons why we do not include Psalm 151 in most Bibles. One is that the psalm was not part of the traditional or Masoretic Hebrew text. Traditional Judaism considers Psalm 151 to be part of the Apocrypha. Another is that, even though Psalm 151 appears in the Septuagint, the translators of that version marked it as “not of the number”; that is, they did not consider Psalm 151 to be an official part of the biblical canon.
You can read Psalm 151 online at https://www.biblegateway.com/passage/?search=Psalm+151+1&version=CEB