According to Carter Burwell’s website, he will not be composing music for the New Moon soundtrack.

As I understand it, the director of New Moon, Chris Weitz, has hired Alexandre Desplat to composer the music for the film. Desplat composed the music for Weitz’ earlier film The Golden Compass. I don’t know if they’ll use any of my themes from Twilight, such as “Bella’s Lullaby”.