Select Permissions Across Multiple Schemas Within the Same Database
Granting select permission on the view would be sufficient if the view and tables all had the same owner. This is called Ownership Chaining:


  When an object is accessed through a chain, SQL Server first compares the owner of the object to the owner of the calling object. This is the previous link in the chain. If both objects have the same owner, permissions on the referenced object are not evaluated.


Where the objects have different owners, ownership chaining does not work.

So, the simplest answer is to change the ownership of the tables to match the view:

ALTER AUTHORIZATION ON Pupil.Table1 TO dbo;
ALTER AUTHORIZATION ON Provider.Table2 TO dbo;
ALTER AUTHORIZATION ON Security.Table3 TO dbo;


Granting select on the view:

GRANT SELECT ON dbo.vTestPermissions TO USER = 'your_user';


...will then allow access through the view, via ownership chaining, while preventing direct table access.

If that is not suitable for your needs, we will need to look at a more complex arrangement.