There are 3rd-party tools (with cost) to try to sync these two calendars. Usage would require risk assessment by the IT Solutions security team.
If one must use calendars in both systems, it is recommended to use a third party device & application (such as a mobile phone calendar) to "sync" the calendars (i.e. to see both calendar feeds simultaneously) while managing the events in the calendar to which they are part (e.g. Google or Outlook) using the web-based applications on their desktop.