Android - How to update TWRP from within TWRP?

Downloading coming from the list of devices allows to download a .img image which can be transferred via MTP-USB connection and installed after selecting Images in the Install file browser. When asked to select between boot and recovery partition select the recovery partition (selecting the boot partition has at least no effect and might be harmful).

It's possible to flash a newer version via fastboot as well.

TWRP can be updated within TWRP recovery itself, by flashing the latest image. Alternatively, TWRP can also be updated via Flashify and Official TWRP apps. It is a simple way to update without using a pc.

Refer here for detailed guide -How to update TWRP to latest version without PC.