Heres a guide i took from Reddit.Edited with additional info and some links.
Proceed with caution
1) Download a Developer fastboot ROM
I used - kate_global_images_6.9.29_20160805.0000.29_6.0_global_9aa2d85137 which can be downloaded from here -
http://en.miui.com/thread-370585-1-1.html
2) Decompress it and head into the images folder. (Rename the archive's extension from .tgz to .tar.gz before extracting if you're having trouble with missing files)
Note 7zip works well for this
3) Make a backup of the original folder and Replace the recovery.img file with your TWRP image. Has to be named as recovery.img
Connect your phone in EDL mode. (adb reboot edl)
Recovery files can be downloaded here :
http://forum.xda-developers.com/redmi-note-3/how-to/guide-redmi-note-3-available-twrps-t3406708 rember to extract the .img file out of the zip file for this to work
4) Point MiFlash to this folder and flash it.
After ~400 seconds and the flash is successful, unplug the phone. Do not boot the phone normally yet. Instead, boot into TWRP by pressing the Volume Up and Power keys together.
5) Allow anything TWRP asks you. This typically means disabling the stock recovery from overwriting your newly flashed custom one.
Do not flash CM13 or anything yet.
!NB! Use ALKA Twrp to backup ALL partitions.Keep that backup safe !NB!
6)Reboot from the main menu into MIUI. This is important. On first boot, MIUI expands the filesystem to use up all available storage.
You now have TWRP permanently installed without any bootloader unlocking necessary.
Flash whatever you want, treat the phone as if it were unlocked.
You can return the device back to factory defaults by flashing the original firmware using EDL mode.
Normal recovery and regular MIUI
For those that just want root access,after you have a room with TWRP,enable OTA survival in TWRP,flash Systemless root from XDA and update to the latest version
If you want CM13,I suggest you read this entire post -
http://forums.whirlpool.net.au/archive/2566258
I could make a quick guide however I feel like the Q&A in there covers everything better than a guide could