Melt butter in a large pot over medium heat. Add onion, celery and fennel and season with salt and pepper. Cook until softened, 8-10 minutes.
Stir in garlic and cook until fragrant, 1 minute. Whisk in flour and cook for 1-2 minutes. Gradually whisk in the vegetable stock, then add the cream and reserved clam juice. Bring to a boil, reduce to a gentle simmer. Cook for about 10 minutes to thicken and let flavors meld, seasoning with salt and pepper to taste.
Add potatoes and cook uncovered until potatoes are tender, about 10 minutes. Stir in clams and gently cook another 5 minutes. Remove from heat; stir in peas, chives and tarragon. Taste and add more salt or pepper if needed.
To serve, divide among bowls and garnish with reserved fennel fronds.