You should be able to move your original base to your new device, as long as you have linked it to a recovery method, like Facebook, Game Center (iOS Only) or Google (Android Only).
Please follow the article in our Help Center for step by step instructions for how to do this. Account Linking Guide
If you run into any trouble getting this done, then please let us know the name and Player ID of your main base, the name and Player ID of the alternate base you see on your new device, and if you are switching from iOS to Android, or vice versa, and we will be more than happy to take a look and see what you need to do next to get your base moved to your new device.