Preheat a grill to medium high. Tear off 4 large sheets of heavy-duty foil. Divide the sausage among the foil sheets and evenly top with the bell peppers, celery, red onion and garlic. Drizzle with the olive oil and season with salt and pepper. Add 2 thyme sprigs to each and drizzle with the beer. Bring two opposite ends of the foil together and fold twice to seal. Fold in the other sides and seal, leaving room for heat to circulate.
Grill the foil packets, rotating halfway through, until the sausages are charred and the peppers are crisp-tender, about 20 minutes. Carefully open the packets and sprinkle with parsley.