Yes, it is.
You can restrict the Project security level by the user groups.
I believe these documentations below can assist you during this setup:
Basically in the project administration section you can configure the permissions scheme. The 'Browser Project' permission it is the one that determinates who can see the project, you just need to customise which role/group can browse the project.
Generally, the answer to this is to unpick the default setup that tends to grant browse to everyone by default, and rebuild your access with a model that allows you to have people log in without access to everything. Then you'll be able to leave out the protected projects from general view and just grant limited access to them.
Issue security can hide individual issues, and be used to achieve much the same without rearranging the default access.
The defaults in Jira is to have the group "jira users" used for both saying "this person can log in" and "this person is in the role of users in the project and hence, can see it". In new Jira installs, it's quite easy to get rid of this and enable a simple access model, but if you've drifted into using the defaults, it can be quite a large job to separate "log in" from "see every project"
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