Normally, you have to firstly unlock the bootloader of your Redmi Note 3 in order to install TWRP and gaining root access by flashing SuperSU through TWRP. Yes indeed there has been a workaround to unlock Redmi Note 3 bootloader using unofficial method without having to apply for official permission. However, it still has risks to eventually end up bricked.
Here in this page, you’ll see a package called root_folder.zip containing all necessary files to flash TWRP on locked Redmi Note 3 without complicated process. Created by one of MIUI Device Team members, the tool will perform temporary bootloader unlocking mechanism. Consequently, that temporary unlocked state will lead the way to install custom recovery (TWRP) and root the device.
Please note! This tool is developed only for the Qualcomm Snapdragon variant of Redmi Note 3.
How to install? Follow this guide to root Redmi Note 3 SD with no unlock permission.
What’s in the package?

Also read : Automatic Root Tool for Redmi Note 3.
Download
File name :
root_folder.zip
Version n/a | 6996 downloads | 44 MB
File name :
safe_emmc_appsboot.mbn
Version n/a | 5203 downloads | 562 KB