Hi Derek, you can make a project private by limiting it's users & roles. If you're a JIRA admin, you can access these settings by clicking on the gear icon in the top-right, then selecting 'Projects'. Once the page loads, click on the project you want to update, and go to the 'Users and roles' section of the project settings. From here you can add a new user to a specific role by selecting the 'Add users to a role' option in the upper-right, enter the desired user and select the appropriate role, then click 'Add'. You can also remove users/roles from the list of existings users/roles by hovering over the user/role and clicking the trashcan icon.
Here's a couple of help articles that should give you further details on this process:
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