At the moment, we do not have the ability to set permissions beyond the whole database level for editing and viewing.
Users can apply filters in Databases and there is no way to restrict them.

This suggestion to allow restricting filters based on the user's access level to the Database. 

For example: If user has ‘View’ access only, they wouldn’t be able to access filters.

This will allow creators to create a view of Databases for certain users instead of showing the complete Database.