Hi Kyle - You will have to do some setup around the 'Custom Properties' (Setting up advanced security rules - Qlik Sense - YouTube) within Qlik to do what you are asking about. We have a similar setup where we are using the AD groups to assign application level (Qlik) permissions as well as permissions to various Qlik apps. You cannot bring AD groups in to the Qlik environment but the users you sync up using the AD connector will have their group memberships. You can setup security rules using the built-in user properties along with the custom properties.
Example: ((user.group=resource.@Positions and user.group=resource.@Area and user.group=resource.@Streams))
This would provide read access to applications where the AD group membership of a user matches the assigned custom property of the application.
Hope this helps.