Heat the oil in a medium non-stick saucepan over a low heat. Add the onion and garlic then cook, stirring frequently, for about 7 minutes or until the onion is tender. Add the celery and carrot then cook, stirring frequently, for a further 5 minutes or until the carrot is tender.
Stir in the wild rice. Add the carrot juice, water, pepper and thyme then bring to the boil. Reduce to a simmer then cover and cook for 1 hour or until the wild rice is tender (check after 45 minutes).
Meanwhile, toast the walnuts in a small frying pan over a low heat, stirring frequently, for about 5 minutes or until they are crisp and fragrant. Stir the walnuts and cranberries into the wild rice just before serving.