Short answer is – No! it cannot be done.
By way of some background, the way an ical feed works is that it is your calendar application (Google Calendar in this case) which periodically requests an update of the information from Clinicea i.e. Clinicea does not and cannot push the data to your calendar.
Google Calendar does not currently offer either a user-configured auto-refresh interval or a manual refresh option. Even though the Google Calendar interface has a refresh icon, this button does not update subscribed feeds in Google Calendar, only your local Google Calendar. Currently, subscribed calendars may take up to 12 hours to be updated in Google Calendar as stated in their documentation here: https://support.google.com/calendar/answer/37100?hl=en&ref_topic=1672445
In case you are using an apple calendar, or a Microsoft Outlook calendar or some other company’s calendar software, there still might be some hope for you.
Workaround for Android Devices
A workaround for android devices is available, by way of installing an app called iCalSync. It seems to work.
In May 2015 Google have altered their timeframe for update from 8 hours to 12 hours – which seems to indicate it’s an ongoing problem which seems to be getting from bad to worse.
Anyways you can take comfort in the fact that you’re not alone – here’s a thread on Googles forums that’s been running for over 4 years of people complaining about feeds not updating Google Calendar not updating published calendar added by URL