In a food processor, combine tuna, garlic, chives, salt, thyme, and lemon zest. Pulse to chop and combine until a coarse mixture is formed. Form 4 patties and place on a greased sheet pan. Cover with plastic wrap and refrigerate at least 1 hour or overnight.

Cook burgers on a preheated grill or grill pan for 15 to 18 minutes per side or until cooked through. Remove from grill and let rest for 5 minutes. Place each burger on a kaiser roll with 1 tablespoon mayonnaise, 2 tablespoons Black Olive Tapenade, and a few arugula leaves.