Composer

Stagework says:

The composer is the creator of all the original music in a play. This can take the form of incidental music to support the action, an integral component of the production, or featured compositions or songs as with a musical.

Music can play many roles in drama, for instance it can underline or heighten mood, punctuate and drive the action forward, or provide a counterpoint or commentary on the action. The composer works closely with the director, the cast and also the sound design team who produce sound effects.

As with a film, the music may be written separately and brought together with the action of a play, or developed during the course of rehearsal to match the action.