Hello J3r0m3.qU3k,
Thank you for reaching out to the Microsoft Community. My name is Gunasekar and I'm happy to help.
- As the owner, after adding a tab in Teams, will it show up for all members automatically or members themselves have to add the tab ?
As a team owner, when you add a tab in a channel, it becomes immediately visible to all team members. There's no need for them to add it themselves—it will appear in the channel's navigation bar.
- How to restrict such that members can add Tab, but not remove them?
Members are the people in the team. They talk with other team members in conversations. They can view and usually upload and change files. They also do the usual sorts of collaboration that the team owners have permitted.
If you’re a team owner, you're in control of many settings and permissions of your team. The following describes how to adjust them.
• Go to the team name and select More options >Manage team.
• In the Settings tab, check or uncheck the options or permissions that you want to use.

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I hope this information helps. If you have any questions, please let me know and I will be happy to help you further.
Best regards,
Gunasekar N