Today December 2nd I received this message from Telegram service notifications about my outdated Desktop app version:
Please update your app to the latest version. The version you are using is out of date and will stop working soon.
...In Ubuntu 20.04.3 LTS the latest released version of Telegram Desktop app is 2.1.7, I ask to you for upgrade soon the repo for LTS with the last version of Telegram, please!
Here is a related question for ARM.
If the source you have isn't updated, you could file an issue and perhaps the maintainer will update it. Of course, make sure your system is up to date first (sudo apt update && sudo apt upgrade).
Before trying any of these, remove whatever you already have. If you edit your question to include how you installed it, we can try to help you undo that.
There are a multitude of ways to get the updated version. I've ordered these best-to-worse (in my opinion)
The official download link - Warning: direct download. It produces a tar.xz. See this other question for the ways to extract it. Tl;dr: tar xf archive.tar.xz (credit to @ramslök for that)
The snap package - Snap is a quick and easy way to install packages, and installing Telegram via Snap is very simple
Flatpak - Flatpak is good as well, but I find that Snap is better supported by default in Ubuntu, so I'd suggest Snap over Flatpak
Un-official PPA's - There are some unofficial PPA's like this one, but unless you have a really good reason to not use the three official methods, I don't suggest this. Regardless, here is how you would add that one
$ sudo add-apt-repository ppa:atareao/telegram
$ sudo apt-get update
$ sudo apt-get install telegram
update your telegram desktop to visit the store https://snapcraft.io/store or update via command line
sudo snap install telegram-desktop
sudo apt update
