Preheat oven to 350 degrees. In a medium skillet, heat oil over medium. Add onion, garlic, and celery and cook, stirring occasionally, until vegetables are soft, 7 minutes. Season with salt and pepper.
In a large bowl, combine vegetables, turkey, egg, bread, 1 1/4 teaspoons salt, and 1/2 teaspoon pepper. Using your hands, mix until combined. Mix in feta and dill. Transfer to a parchment-lined rimmed baking sheet and form into a 4-by-10-inch loaf. Bake until cooked through, 45 to 55 minutes, rotating sheet halfway through. Let rest 10 minutes before slicing.