How to transfer Clash of Clans from one iOS device to another
Yes it is possible. All you need to do is have both your devices next to that you want to make the transfer with. Then tap the settings button in clash of clans and you will see "link a device". Follow the on screen instructions after that.

If you have a new account already made on your new device past town hall 4 you are unable to link them. You will need to contact supercell for further information, which is what I had to do.