Is there a way to have a Jira project only visible to select members?

[josuetello]

You can go to the project settings and navigate to the "Users and Roles". here you can set which individual members or groups have access to the project. Alternatively you can go to Permissions in the project settings in case you are just wanting to limit individuals from being able to perform specific actions.

[Nic Brough -Adaptavist-]

Yes - have a look at the permission scheme, changing the "browse project" rule so that it only includes the people you want to let into the project.

[Alexey Dorofeyev]

Members of what?