Make sure you have the Clippy switch turned on. Your device will only receive/send new clipboard content if your device has the switch is turned on.
For Android devices, due to system restrictions, App can not listen to the Clipboard Changes. For that, you need to use the context menu to select Copy to Clippy instead of simple Copy. And if that option is not visible on your device (due to different OS-level configurations), you can click on Share and select "Copy to Clippy". Both the action will update the clipboard on your device as well as send the content across your devices.