Why is this song 'new'? It celebrates something that has just been accomplished, a victory hard-won.
The elders sing a 'new song' because it's a song of redemption, a theme that couldn't be fully celebrated until Christ's work was completed. Before His sacrifice, redemption was anticipated; now it's a reality. This emphasizes that worship isn't just about acknowledging God's eternal nature, but also His powerful, specific actions in history, particularly the saving work of Jesus.
This new song highlights the finished work of Christ: 'for You were slain, and You ransomed people.' This isn't a song of hope for what might happen, but a triumphant declaration of what has been done through His death and resurrection.