Pat pork dry. Melt reserved fat in heavy large skillet over medium-high heat.
Add pork and brown well on all sides. Sprinkle with salt and pepper
Add wine, stock (can substitute with sodium free chicken stock), onions, carrot and garlic and bring to simmer. Cover and cook 30 minutes, adjusting heat so cooking liquid is barely shaking.
Add chestnuts and leeks to port. Continue cooking until instant-reading thermometer inserted in pork registers 170F and vegetables are tender, about 30 minutes; do not overcook.
Strain liquid into heavy medium saucepan. Boil liquid until reduced to thin sauce like consistency; degrease.
Return to vegetables. Slice pork and arrange around platter. Spoon vegetables and sauce into center and serve.