Preheat a 5- or 6-quart air fryer to 400°F for 3 minutes.
Halve the new potatoes.
Trim and scrub the unpeeled carrots; cut any larger carrots in half lengthways.
Separate the unpeeled garlic into cloves.
Place the potatoes, carrots, and garlic in a large bowl with the remaining ingredients.
Season with salt and pepper, and toss everything to combine.
Carefully pull out the air-fryer pan and basket.
Place the seasoned vegetables in the basket.
Slide the pan and basket back into the appliance.
Keep the temperature set at 400°F and set the timer for 20 minutes.
Turn the vegetables halfway through the cooking time to ensure they cook evenly and become golden and tender.