Legends at War
On your old device, go to Menu > More. Select GameCenter. This will link the old account with your GameCenter account. (If you do not yet have a GameCenter account, you will need to exit the game, open that app on your device and create an account, then return and follow these steps.)
Once linked, it's time to move the old account to the new device. On the new device, log into GameCenter. Now open the game. The option of syncing an existing account should be given. Say yes and the old Legends at War account should now be on the new device!