Preheat the air fryer to 375°F (190°C).
In a mixing bowl, combine the shredded chicken, Alfredo sauce, mozzarella cheese, garlic powder, Italian seasoning, salt, and pepper. Mix until all ingredients are well combined.
On a lightly floured surface, roll out the pizza dough into a rectangle about ¼ inch thick. Cut the dough into 4 equal squares.
Place a generous scoop (about ⅓ cup) of the chicken Alfredo mixture in the center of each square.
Fold the dough over the filling to create a pocket. Press the edges together firmly to seal. You can crimp the edges with a fork for a decorative touch.
Brush the tops of each calzone with olive oil and beat the egg in a small bowl. Use the egg wash to brush over the top of the calzones for a golden finish.
Place each calzone in the air fryer basket, ensuring they are not touching. You may need to do this in batches.
Air fry for 10-12 minutes, or until the calzones are golden brown and cooked through.
Once done, carefully remove from the air fryer and let them cool for a minute before serving.