Does the iPad Air support Wi-Fi Direct?
Whilst the device hardware does support Wi-Fi Direct, the limitation in this case is software.

There is currently no software on iOS that connects to a wireless hard drive through Wi-Fi Direct, but that hasn't stopped apps being developed to take advantage of this — Seagate has an app that connects to wireless hard drives:


http://www.seagate.com/gb/en/services-software/apps/seagate-media-app/