¡Hola!
The subject of this sentence is a person, which means that the third-person singular would need to be used.
The conjugations for "trabajar" (to work) are:
Yo- Trabajo
Tú - Trabajas
Él / Ella / Usted - Trabaja
Nosotros / Nosotras - Trabajamos
Ellos / Ellas / Ustedes - Trabajan
Since Edward can be replaced with Él (third person), "trabaja" is most appropriate in this situation.