If you have any leftovers, store the meat in an airtight container in the refrigerator for three to four days. You can store the turkey legs whole or shred the meat off the bone. Freezing leftover meat is always a great option. In that case, I like to shred the meat first and keep it in a freezer-safe container or zip bag for four to six months. After that, the meat is still safe to eat, but the quality starts to degrade. The leftover meat is perfect for tacos, enchiladas, mac and cheese, salads, sandwiches — you name it.