In a large pot over medium-low heat, cook diced bacon until lightly crisp. Add butter and melt.
Add leek and cook 5–7 minutes until soft. Stir in garlic and cook 1 minute.
Sprinkle flour over the mixture and stir 1–2 minutes.
Slowly stir in bottled clam juice and reserved canned clam juices. Add potatoes and bay leaf.
Simmer gently about 10 minutes, until potatoes are fork-tender.
Reduce heat to low. Stir in milk, cream, and clams; warm gently without boiling.
Remove bay leaf, stir in tarragon, season to taste, and rest 5–10 minutes before serving.