Can I transfer a 2007 factory installed Home-LINK mirror into a 2016 Kia Sportage?
You don't have the wiring in the 2016 to support the old device.
The power connector is different. You could take the lead from the 2016 and cut the connector off and put on compatible connectors. All you need for the old link device is power and a ground, if I am looking at the correct one.
If you are willing to DIY your electrical system and deal with the results you can pull this off but it will not 'plug and play'.