As far as I can recall, the few zombies in the Discworld are basically people who were just too stubborn or bloody-minded to die.
There's a very old zombie lawyer who basically is the arch-lawyer of the city.
There's a zombie policeman, who I believe sometimes doubles as an undead-rights activist.
There was a zombie wizard, but he only hung around for a little while.
None of them professed any desire to eat brains.