The Kubuntu team announced today that the KDE Plasma 5.22 packages are available in the Kubuntu Backports PPA repository, along with the latest versions of the KDE Frameworks and KDE Gear software suites.

Let's see how you can upgrade:
First you need to add the Kubuntu Backports PPA. To do this, you need to open a terminal (Konsole) and run the following command.
sudo add-apt-repository ppa:kubuntu-ppa/backports
Press the Enter key when prompted and wait for the command to complete.
Once the installation of the command is completed, you can request the update with the following command:
sudo apt update && sudo apt full-upgrade
Alternatively, you can use the Discover package manager to install these updates if you do not like the commands from the terminal.
Whichever method you choose, you will have to wait for all the new packages to be downloaded and installed.
After downloading and installing all the packages, you will need to restart your computer and you will have KDE Plasma 5.22. From now on you will continue to receive newer releases as they are published by the KDE Project.
The next scheduled release, KDE Plasma 5.22.1, is scheduled for June 15, 2021 and will be available at Kubuntu Backports PPA repository shortly after its release.
