Keep alligator tenderloin meat frozen until you're ready to use it.
For thawing tips, please read Safely Defrosting Frozen Food for Maximum Flavor.
Alligator has a high water content so it is best sautéed. Many people recommend marinating alligator meat to further tenderize it. However, be warned: marinating excessively will completely cover the distinctively delicious flavor. Whether marinating or not, be sure to pat the meat dry prior to cooking it for a better sear.
Alligator can also be pounded and served with a savory sauce. It is delicious when added to a gumbo or fried.
When considering how to cook your gator meat, keep in mind that alligator (like squid) is best cooked either very quickly or very slowly on low heat (stewing or braising). Doing so will keep the meat tender.