Heat olive oil in a large pot over medium heat. Add onion, celery, and carrots and cook until softened, about 5-7 minutes.
Add garlic and cook for 1 minute more.
Stir in flour and cook for 1 minute.
Gradually whisk in clam juice and bring to a boil. Reduce heat and simmer for 10 minutes.
Add potatoes and simmer until tender, about 15 minutes.
Stir in clams and cook until they open, about 5 minutes. Discard any clams that do not open.
Stir in heavy cream, parsley, salt, and pepper. Heat through.
Serve hot.