Definition and Significance:
The term "A New Song" in the Bible refers to a fresh expression of praise and worship directed towards God. It signifies a response to God's mighty acts, His deliverance, and His ongoing work in the lives of His people. The concept of a "new song" is often associated with renewal, transformation, and the anticipation of God's future acts of salvation and justice.

Biblical References:

1. Psalm 33:3 · "Sing to Him a new song; play skillfully with a shout of joy."
This verse encourages believers to offer a new song to God, emphasizing skillful and joyful worship. It highlights the importance of creativity and excellence in worship as a response to God's greatness.

2. Psalm 40:3 · "He put a new song in my mouth, a hymn of praise to our God. Many will see and fear and put their trust in the LORD."
Here, the psalmist speaks of a personal experience of deliverance, resulting in a new song of praise. This new song serves as a testimony to others, leading them to reverence and trust in God.

3. Psalm 96:1 · "Sing to the LORD a new song; sing to the LORD, all the earth."
This call to sing a new song is extended to all the earth, indicating the universal scope of God's reign and the global call to worship Him. It reflects the anticipation of God's righteous judgment and His salvation reaching all nations.

4. Psalm 98:1 · "Sing to the LORD a new song, for He has done marvelous things; His right hand and His holy arm have worked salvation for Him."
The new song here is a response to God's marvelous deeds and His work of salvation. It celebrates God's power and faithfulness in delivering His people.

5. Psalm 144:9 · "I will sing to You a new song, O God; on a harp of ten strings I will make music to You."
This verse expresses a personal commitment to worship God with a new song, using musical instruments to enhance the expression of praise.

6. Psalm 149:1 · "Hallelujah! Sing to the LORD a new song, His praise in the assembly of the godly."
The new song is to be sung in the community of believers, highlighting the corporate aspect of worship and the shared experience of God's people in praising Him.

7. Isaiah 42:10 · "Sing to the LORD a new song, His praise from the ends of the earth, you who go down to the sea, and all that is in it, you islands, and all who dwell in them."
This passage extends the call to sing a new song to the entire creation, emphasizing the inclusivity of God's salvation and the call for all to participate in His praise.

8. Revelation 5:9 · "And they sang a new song: 'Worthy are You to take the scroll and open its seals, because You were slain, and by Your blood You purchased for God those from every tribe and tongue and people and nation.'"
In the heavenly vision, the new song is sung to the Lamb, Jesus Christ, celebrating His redemptive work and the gathering of a diverse people for God.

9. 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 144,000 who had been redeemed from the earth."
This new song is exclusive to the redeemed, signifying their unique experience and relationship with God. It underscores the theme of redemption and the special status of those who belong to God.

Theological Themes:
The concept of a "new song" in the Bible is rich with theological significance. It reflects themes of renewal, redemption, and the transformative power of God's actions. The new song is often associated with God's deliverance and the anticipation of His future acts of salvation. It serves as a means of testimony, drawing others to faith and worship. The new song also emphasizes the communal and universal aspects of worship, inviting all creation to join in the praise of God.