New mercies from God make us want to sing new songs: Read this article by David Mathis.

Psalm 33:3 Sing to Him a new song; Play skillfully with a shout of joy.
Psalm 40:3 He put a new song in my mouth, a song of praise to our God; Many will see and fear and will trust in the LORD.
Psalm 96:1 [ A Call to Worship the LORD the Righteous Judge. ] Sing to the LORD a new song; Sing to the LORD, all the earth.
Psalm 98:1 [ A Call to Praise the LORD for His Righteousness. ] [ A Psalm. ] O sing to the LORD a new song, For He has done wonderful things, His right hand and His holy arm have gained the victory for Him.
Psalm 144:9 I will sing a new song to You, O God;Upon a harp of ten strings I will sing praises to You,
Psalm 149:1 [ Israel Invoked to Praise the LORD. ] Praise the LORD!Sing to the LORD a new song, And His praise in the congregation of the godly ones.
Isaiah 42:10 Sing to the LORD a new song, Sing His praise from the end of the earth! You who go down to the sea, and all that is in it You islands, and those who dwell on them.
Revelation 5:9 And they sang a new song, saying, " Worthy are You to take the book and to break its seals; for You were slain, and purchased for God with Your blood men from every tribe and tongue and people and nation.
Revelation 14:3 And they sang a new song before the throne and before the four living creatures and the elders; and no one could learn the song except the one hundred and forty-four thousand who had been purchased from the earth.