How do we restrict certain jira administrators from seeing a project?

Elisabeth Gie

We have a project for our HR department, they have to input salaries etc 

The JIRA administrators are not added to the project but due to the nature of the JIRA administrator permission, they are able to add themselves to the project which means they can see the employees salaries.

Is there a way to restrict which JIRA administrators can actually add themselves to this HR project?

Nic Brough -Adaptavist-

No.

They need admin rights in order to do their job of administration, and that includes the right to change permissions and memberships. 

If you don't trust your admins, you have a problem, and it's probably a lot wider than just JIRA.  You have to trust them, or one of your HR people is going to need admin skills, so thy can take over the job and sack the admin.