We got root on the Verizon Galaxy Note 3 just a few days ago, but we don't even need that to wifi tether on this device for free! It is actually pretty simple to tether using the native app on the Galaxy Note 3.
Go To Settings, More Settings, Mobile Hotspot, Configure (Choose a wifi hotspot name and password)
Go To the Play Store and Grab the Hotspot Toggle Widget
Place the Widget On your homescreen
Tap the Widget to Toggle hotspot on
When the notification pops up asking you to subscribe just hit the home button
You are now tethering for free