In a mixing bowl, combine the shredded chicken, Alfredo sauce, garlic powder, Italian seasoning, salt, and pepper. Mix well until the chicken is coated in the sauce.
Preheat the air fryer to 375°F (190°C).
On a clean, floured surface, roll out the pizza dough into a circle (about 6 to 8 inches in diameter).
Spoon about ¼ of the chicken Alfredo mixture onto one half of the dough circle, leaving a small border around the edges. Top with about ¼ cup of shredded mozzarella cheese.
Fold the other half of the dough over to create a pocket, sealing the edges by pressing with your fingers or a fork.
Repeat the process with the remaining dough and filling to create a total of four calzones.
If desired, beat the egg and brush it over the calzones for a golden finish.
Place the calzones in the air fryer basket, ensuring they are not overcrowded (you may need to do this in batches).
Cook the calzones in the air fryer for 10-12 minutes or until they are golden brown and crispy.
Carefully remove the calzones from the air fryer, let them cool slightly, and serve with additional Alfredo sauce for dipping, if desired.