Render salt pork in large pot. Remove from pot when salt pork is brown, about 5 minutes.
Add butter or olive oil, onions, and celery. Cook until onions are translucent, about 3 or 4 minutes. Add flour to pot and stir with onions and celery; stir constantly for about 2 minutes.
Add clam juice, potatoes, and thyme and bring to a boil; stir constantly. Reduce heat and cook until potatoes are tender, about 10 minutes.
Add clams and half-and-half and return to a boil; reduce heat. Season with salt and pepper as desired. Serve with crackers or hard rolls.