We recommend that that this alligator meat is thawed and cooked all at once. Then perhaps you can freeze it and store it for later. Thawing the pack and then refreezing raw portions can compromise the meat's quality.
For thawing tips, please read Safely Defrosting Frozen Food for Maximum Flavor.
Alligator leg and body meat is excellent for use in soups, stews and sauces. Be sure to pat the meat dry prior to cooking it for a better sear.
When considering how to cook your alligator 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.