What area for extra capabilities do you mean?

In order contributor can add a feature image he should have the ‘upload_files’ user capability. This automatically gives him access to the Media Library.
It’s possible to block for the contributor role the access to the “Media” menu with “Admin menu access” add-on.
But if you fully block “Media” menu (including “Add new”) user will can not add new image. It will can just select a featured image from the existing images.
I offer do not block “Media” menu for contributor. It’s possible to restrict him to see just his own images there. Activate “Edit posts restrictions” add-on. Do not forget to add ‘create_posts’ capability to ‘contributor’ role in this case.
Open “Posts Edit” dialog for contributor role and select “Allow”, “Own data only”. This setting will hide from the Media Library images uploaded by other users.