ChamOSAndroid supports in-app updates. ChamOS checks the manifest for its update channel, downloads and verifies the package, then asks the system installer to confirm installation.
If Android asks you to allow ChamOS to install apps, grant that permission and continue. The stable app follows the stable channel; the beta follows the beta channel.
You can also download the package for the same channel from the official website and install it over the existing app. Do not uninstall first, because doing so can delete local data.