Thaw the puff pastry sheet at room temperature for 30 to 40 minutes, until it unfolds without cracking. Preheat the air fryer to 400°F and line the basket with parchment paper.
Roll the pastry to fit your basket, about 10x14 inches, pressing the fold creases flat. (Tested in an Instant Pot Omni air fryer.)
Score a border ½ inch in from the edge with the tip of a knife, cutting only halfway through. Prick the center several times with a fork.
Brush the pastry lightly with olive oil and transfer it to the prepared air fryer basket. Air fry at 400°F for 7 to 10 minutes, until puffed and golden.
While it cooks, wash and thinly slice the tomato, olives, and red onion. Blot the tomato slices dry.
Remove the crust and gently press down the center if it has puffed. Spread the pizza sauce evenly inside the scored border.
Top with mozzarella, then the vegetables. Return to the air fryer at 400°F for 5 to 8 minutes, until the cheese is bubbling and the border is deep golden. Don't overload the pizza — excess toppings cause a soggy base.
Garnish with fresh basil and serve warm.