Heat 1 tablespoon of the oil in a large, heavy-bottomed saucepan over medium. Add sausage, and cook, stirring often with a wooden spoon, until sausage crumbles and is cooked through, about 5 minutes. Using a slotted spoon, transfer sausage to a plate lined with paper towels to drain, reserving drippings in saucepan.
Stir in flour and remaining 2 tablespoons oil with a wooden spoon, and cook, stirring constantly, until mixture turns deep golden brown, about 10 minutes. Add onion, bell pepper, and celery, and cook, stirring often, until onion is translucent, about 4 minutes. Add garlic, and cook, stirring often, until fragrant, 1 minute. Add stock, stirring with a wooden spoon to loosen any browned bits from bottom of pan. Bring to a boil.
Stir in collard greens and cooked sausage; reduce heat to low, and simmer, stirring occasionally, until greens are tender, about 45 minutes. Add shredded turkey, and cook until heated through, about 5 minutes. Stir in salt and pepper. Spoon stew over hot cooked rice, and serve with hot sauce.