If you are on Android device, first recommend use the pull-to-refresh feature on the Meditate screen: if you open the Meditate screen and drag your finger downward on the page, a loading icon should appear that will refresh the content. This feature refreshes all content on the Meditate screen as well as the home screen, so it should work to update the Daily Calm for you.
If you are on iOS, or the above does not work, I recommend hard-quitting the app (or force stopping it), and ensure that you are connected to a strong WiFi or data signal when you do so. This should force a refresh on the Daily Calm. You can also try logging out and back in to your account to sync the meditation.