Hi Charlotte,
Unfortunately we don't have a way to define an access permission on custom fields. At the moment custom fields can only be shown/hidden on a project-by-project basis. The user's permissions in each project is what will determine the access level, so Viewers will have a read-only access to the field, while Editors and Admins will have a Read-Write access to the field.
This, in my opinion, is also a good enhancement request. Enhancement requests are posted are our ideas site. This site requires a username. If you don't have one then please email to: ac-ideas@ca.com and we shall create one for you.
Thanks,
Sagi