The concept of a ‘new song’ in the scriptures is usually with reference to extraordinary occasions worthy of thankful praise include celebration and commemoration of the grace & glory of God upon securing victory for His people despite existential threats and peril.  Think of the songs on the lips of those who were the first to receive immanent news of the incarnation… Many, Zechariah, Simeon wrote the first Christmas Carols as ‘new songs’ praising God & welcoming their messiah.  Today’s psalm is not one of these precisely, rather it contains a vow to write such a song upon answers to David’s plea for the salvation of himself and his people.  Languishing under the threat of his enemies David longs for the day his deliverance will occasion further music.  In the meantime therefore, Psalm 144 is a new song song written in supplication for such a time.