In a glass baking dish or a wide, shallow, nonreactive bowl, mix together olive brine and lemon juice. Gently toss in tuna slices and olive slivers. Cover and refrigerate for 2 hours, occasionally moving tuna slices around gently in marinade to ensure that slices cure evenly.
Just before serving, strain the tuna slices from marinade. Divide tuna between 4 to 6 appetizer plates. Spoon a little marinade (with olive slivers) over the tuna. Grind black pepper, to taste, over each serving. Garnish with fennel and lemon zest, and serve immediately.