Enable WiFi when a specific application needs it, then disable after N minutes I do not leave WiFi nor data transfer enabled on my Samsung Note 3. The only application that I would like to have access to the network is Ankidroid.

Is there any way to have WiFi automatically enabled when Ankidroid requests network access, and then have WiFi automatically disabled (perhaps after N minutes)?

Right now I am enabling Wifi, syncing Ankidroid, and then disabling Wifi manually. It would be nice to automate at least part of this process.
Good. In this case you may try Tasker from App Store (However there are free trail available). Set your profile that triggers when the Specific App (Ankidroid) is Opened, and write a simple task

Proile:
1. App-> Ankidroid

Task:
1. Enable WIFI
2. Wait N Seconds
3. Disable WIFI

Tasker need some learning curve though, but it is very powerful and you can automate anything in your phone!