This is a modified version of the driver from here:
http://www.tp-link.com/us/download/TL-WN722N.html#Driver
http://static.tp-link.com/TL-WN722N(US)_V2_161112_Linux.zip
Warning - Experimental
I'm not an experienced driver or kernel programmer. Use at your own risk.
It's not picking up any wireless N networks, but seems to be working with 2.4ghz networks.
Instructions, tested on Ubuntu 16.04 with 4.4.0-59-generic #80-Ubuntu SMP
I'm using a TP-Link TL-WN722N version 2.1.
On Kali ensure your sources.list has the deb src line uncommented
nano /etc/apt/sources.list
and then run
apt-get update
apt-get install linux-headers-$(uname -r)
apt-get install binutils
apt-get source linux-image-$(uname -r) # this will download source to PWD
apt-get build-essential
There may be one or two packages I missed, but that should cover most of it.
cd into your kernel source.
cp /usr/src/$(uname -r)/Module.symvers .
cp /boot/config-$(uname -r) .config
# Export the path where you downloaded the source.
export KSRC=$PWD
cd back to this project.
make
sudo make install
sudo modprobe -f 8188eu
sudo modprobe 8188eu
With any luck, you should now have a working wireless device. As soon as I loaded the module on my system, Ubuntu picked up the wireless networks.