Heat olive in frying pan over medium high heat. Add alligator meat and brown until golden. Remove to slow cooker.
Add more oil, if needed. Sauté celery, carrot and onion until soft. Add to slow cooker.
Add the rest of the ingredients, except corn and shrimp. Slow cook on low for about 4 hours until alligator is tender. Add corn & shrimp, cook for an additional 15-20 minutes until shrimp are pink and opaque.
Notes
Store leftover in refrigerator for 3-4 days.Reheat in microwave for the least amount of time possible, to get it hot enough. 1 minute or so.Leftovers can be frozen. Thaw completely in refrigerator and reheat in microwave.