When you run discovery, you have ability to select a workspace ( a project for data quality/curation). When you go to quality menu on the left bar , you will be able to see the workspace and modify who has access to the workspace and control their access level.
With that, you should be able to govern who can see details and who can edit them.
Having said that, if you have the discovery role, you are able to see high level view of discovery at the moment.
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Kunju Kashalikar
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