Hello @Artur Bogucki this highly depends on the permission schemes within your Jira instance. For your use case it would be ideal, to have a permission scheme that grants users access to a project when they are in a specific project role (for example Users).
In the project role, you can still feel free to add a group containg all relevant peope to grant them their permissions.
In the project that needs to be visible to your specific person, you can then explicitely add them to your project.
Basically you need to follow these steps:
1. Create a group for all people who need to be able to access all projects (e.g. jira-users-internal)
2. For all Projects where this applies, add the people to the role users.
3. Create a copy of your permission scheme to have a backup, and change the copied permission scheme to grant Browse Project Permissions to the project role Users.
4. Swap the Permission scheme in a testing project to the copy, to see if the effect takes place as wanted.
5. If this worked as desired, either swap the scheme back and change the original one, so that you don't have to change the scheme for all projects, or do all the changes to the scheme attached to all projects. This largely depends on what you prefer.
6. For the project where you specific person needs access, add them to the role Users.
Hope this helped 😊
Thank you for your help. In addition to your instructions, I had to remove browse projects permission for Any logged in user and it worked.
I also found a nice tutorial here https://confluence.atlassian.com/cloudkb/how-to-restrict-project-access-for-teams-in-jira-cloud-953142266.html
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