Hi Chief,
To play your village on another Apple device, you need to use your Game Center account.
First, make sure that your village is already linked to your Game Center account on the device that your village is currently on. Then, sign into that same Game Center account on the device that you want to transfer your village to. After launching Clash of Clans, you should be prompted to load your old village.
Please remember that the ‘Link a device' feature is necessary only if you want to transfer your game from an Apple device to an Android, or vice versa.
Remember that each village needs to be connected to a unique Game Center account, as two different villages cannot be saved under the same profile.
I hope this helps, but don't hesitate to let me know if you need some more