If you would like to get all updates faster and be the first to test new features, you are welcome to use Telegram Desktop's beta version updates.
The stable version is updated less frequently, but is tested better than the beta version.
Here are the beta version links for different platforms:
Windows x64 Setup
Windows x64 Portable
Windows on ARM Setup
Windows on ARM Portable
Windows Setup
Windows Portable
Mac OS X 10.13+ Setup
Linux 64 bit with glibc >= 2.28
Just install it on top of your current Telegram Desktop and there you go.
The up-to-date versions of Telegram Desktop support Windows 7 and later, macOS 10.12 and later and 64 bit Linux. But there are old versions available:
v4.9.9 Setup for macOS 10.12
v4.9.9 for Linux with glibc < 2.28
v2.4.4 Setup for OS X 10.10 and 10.11
v2.4.4 for Linux 32 bit
v1.8.15 Setup for Windows XP / Vista
v1.8.15 Portable for Windows XP / Vista
v1.8.15 Setup for OS X 10.6 and 10.7
v1.8.15 Setup for OS X 10.8 and 10.9