Preheat air-fryer to 400°F. Place frozen chicken patties in a single layer in air-fryer. Cook until fully cooked through, or until internal temperature reaches 165°F, about 11-12 minutes. Transfer patties to a plate, and set aside. Place buns inside air-fryer and cook until lightly toasted, about 1-3 minutes. Spread pesto evenly on the bottom of each bun. Top with mozzarella, hot chicken patties, tomato, arugula and lid of bun. Serve hot and enjoy.