How do I refresh a subpanel when a record is added to a different subpanel?

On a case record I create a meeting using the create button on the subpanel. When the new meeting is saved an advanced workflow process creates a new task related to the case record. 

I want the tasks subpanel to refresh when the meeting is added to show the new task when the drawer closes and the user is returned to the case record view. How can this be done?