Is it possible to limit who has access to view parts of my app.
I was to issue an app to the entire organisation but as it uses the same dataset as one that I want to only distribute to a handful of users, is it possible to access control the reports?
You can use Row-level Security and defining that on the Queries powering the report and assign the permission to those that you wish to grant access to on the Service. So if you had the below datasets in your report:
Then add RLS on both datasets and assign users (user 1, 2, 3) on the service and only they will be able to see a populated view of the report, the rest will see 'X' marks on all visuals.
This is the link to RLS: https://docs.microsoft.com/en-us/power-bi/service-admin-rls
Do you publish an App to the whole organization, but there is a dataset inside this App which only a few users should have access to?
If so, nirvana_moksh's suggestion may be helpful.
Addition to his suggestion,
please be aware of that, after publishing Power BI Desktop report to an app workspace within the Power BI service, the roles will be applied to read-only members.
If you have configured the app workspace so that members have edit permissions, the RLS roles will not be applied to them. Users will be able to see all of the data.
Refernce here to set RLS