[Verizon Galaxy Note 3 Q&A, Help & Troubleshooting] Mr. HQ:
Here's directions I found elsewhere on this forum & others using Google

Kingo version 1.1.4.1785 has SuperSU 1.65, I replaced that SuperSU with an updated version. SuperSU Version 1.80 is out now. No issues. Follow the steps below & you'll be up & running. Credit goes to either TomsGT or Kachow I can't remember which so I'll give them both credit

1) Begin by going to the website Root Android phone, flash custom ROM and manage your Android devices, Rooting Freeware Download - Kingo and hit the large green button that reads “Download”. The android_root.exe should begin downloading on Windows 7. Once, it has completed, go ahead, open it and select run. Should receive a box Root Set-up Wizard> select “next”> “I accept the agreement” then next> select the folder for the install, then next> folder selection, then next> create a desktop icon, then next> install> Launch Kingo Android ROOT, finish.

2) This next step can be tricky make sure for simplest use, to have a Micro USB 2.0 cable, Windows 7 computer, USB Debugging enabled. With the Kingo application Launched, there should be a red circle in the middle of screen indicating a device and a computer being connected. Connect both the device and the computer, with both connected, watch the red button turn orange and watch the device for a USB Debugging permission grant to appear and authorize it. Select the “Root” option, watch the screen of your device for the Super User to appear and pop up to authorize ADB Shell> and Grant it (you now have Root), let the rest application run, as soon as device Reboots> DISCONNECT. In fact you can UNINSTALL KINGO FROM YOUR COMPUTER.

3) There’s 2 big steps coming up, one is getting rid of Kingo and replacing it with a pure form of Root and then installing Safestrap, using it to install that pure form of Root. To get started let’s begin with the latest version of SuperSU which is version 1.69. The way this is going to be installed is a different form than usual, as we are actually going to Flash SuperSU. THIS WILL HAPPEN AT A LATER POINT, I WANT TO GET THIS FILE IN POSITION SO WE CAN QUICKLY FLASH IT AND INSTALL IT WHEN THE TIME IS RIGHT. Go ahead and download this file, please save this to the Internal Memory that should read in the folder [ sdcard/UPDATE-SuperSU-v1.69.zip ]. This will be a quick access location.

4) The next step is to install Safestrap, as of today it is running stable which is excellent news, it is also based on TWRP which happens to be a Custom Recovery. Safestrap is Recovery that is designed to work with devices that have locked Bootloaders, in the past years SS was limited to Motorola devices and until recently Hashcode the Developer of Safestrap has transitioned over to the darkside. Hashcode has put thousands of hours into SS and other projects and I owe him the credit to let him explain, here are his two main threads on

Rootzwiki

XDA

After reading Hashcode’s OP’s you should have a complete understanding how to set-up and install SS. I am leaving this section thin as Hashcode does an excellent job explaining how to install SS, what it is, how it works, and all the above. If any questions in specific please ask in this thread.

5) This is the main event, the goal here is to remove Kingo Root and replace it with a Genuine Root. To do this we need to first go into SuperSU app> go under the Settings> scroll to the bottom and find under “Cleanup”/ “Switch superuser app”. Then go ahead and press this area (nothing will indicate that it was pressed.) Then exit SuperSU, if you try to click on the app it will say the app is not installed (this is correct as you will be changing SuperSU momentarily.) Go ahead and Reboot the Device.

6) As the Device is restarting look for the Safestrap Logo Robot to appear, the bottom left corner says “Recovery” and go ahead select it. In the Top Right corner find the “Install” letters in Red> select Storage: Internal Storage (xxxx) /datamedia/media/0 > scroll down and find UPDATE-SuperSU-v1.69.zip, then touch it, on the next screen make sure it is the right file and slide the button to the right to “Swipe to Confirm Flash”. Should be > Successful < if so hit Reboot System.

7) Once, system Restarts> open your app drawer open up SuperSU and Grant any User Apps that you desire.