DO NOT unlink the old account before changing devices. Unlinking it will cause access to the save data to be lost. Before switching devices, please ensure your old account is linked to an existing Google or Facebook account. Install Pocket Pioneers to the new device, and load the game.
On the main loading image, select the account link button:
You will be asked if you would like to load an existing game. Select the platform where your game was linked and it should load your old account to the new device: