Heat olive oil in a large pan with a lid over medium-high heat. Add chicken, season with salt and pepper, and cook until golden brown on all sides, about 6 minutes per side. Remove chicken to a plate.
Reduce heat to medium and add the leek, shallot, garlic, and thyme to the pan. Stir and scrape up any brown bits and cook until vegetables are tender, about 5 minutes. Add cider and tarragon, stir, and return chicken to the pan. Add apples, cover, and cook for 25 minutes. Uncover, increase heat to high, and reduce liquid until the apples caramelize, 3–5 minutes. Sprinkle with the parsley and serve.