Remove beef tenderloin from refrigerator and let sit at room temperature, uncovered, for 30 minutes.
Combine softened butter, grated garlic, rosemary, thyme, sage, salt, and pepper in a small bowl until fully blended.
Pat the tenderloin completely dry with paper towels, then rub olive oil evenly over the entire surface.
Spread the compound butter evenly over all sides of the tenderloin, pressing herbs gently into the surface.
Preheat air fryer to 400°F (205°C) for 3 to 5 minutes.
Place tenderloin in the air fryer basket and cook at 400°F for 5 to 6 minutes to create a seared crust.
Reduce temperature to 350°F (175°C) and cook for 12 to 15 minutes more, or until internal temperature reaches 125°F for medium-rare.
Remove tenderloin from air fryer, tent loosely with foil, and rest for 10 to 15 minutes.
Remove twine, slice against the grain into ½-inch thick pieces, and sprinkle with flaky sea salt before serving.