If you chose Express Installation when you first installed Linux, Parallels Tools were installed automatically after the installation.
Note: You may find the updated list of Linux distributives supported in Parallels Desktop on Apple Silicon Macs here.
If you didn't choose Express Installation, do the following to install Parallels Tools:
Launch the Linux virtual machine.
When it boots up, connect the Parallels Tools image to the virtual machine: in the menu bar, click Devices > CD/DVD > Connect image....
Browse to the image location Application > Parallels Desktop.app > Contents > Resources > Tools > select prl-tools-lin-arm.iso if your Mac runs on Apple silicon or prl-tools-lin.iso for Intel Macs.
This will mount a virtual CD/DVD with the Parallels Tools.
Double-click on the install-gui file to start the installation.
When the installation is complete, click Restart to restart the virtual machine or wait for it to restart automatically.
The details on installing Parallels Tools for Linux using Terminal are maintained and updated in this KB article.
You can easily confirm whether Parallels Tools were installed. Start your virtual machine and look at the status bar of its window. If the tip "Press Ctrl + Alt to release the mouse and keyboard" appears in the status bar of the virtual machine's window, this means that Parallels Tools were not installed. When Parallels Tools are installed, you do not need to press any key to release the mouse and keyboard - they are released automatically.
Parallels Tools may fail to install because not all mandatory packages are available. Check the /var/log/parallels-tools-install.log file in the guest OS for error messages, install the missing packages, and try to install Parallels Tools again.
For more information on installing Parallels Tools, please refer to the Parallels Knowledge Base.
When a newer version of Parallels Tools for Linux becomes available, the Parallels Tools Installation Agent window will appear. You will be prompted to choose the command to gain root privileges and enter the password (if su - root password, if sudo - your user's password). After that, Parallels Tools update automatically.
To reinstall Parallels Tools in Linux, remove them first and install them once again.