Tab Forum question

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For adding a tab for the lasts posts, it depends on how your tabs works. Too many javascript tabs available out there (if what you mean by the tabs is a javascript tabs), and each scripts has each own method.

For displaying the lasts/latest posts in your forum index (no matter whether it's inside a tab or not), you need a plugin for that. If you already have the plugin, you need to edit the template provided by the plugin (again, it depends on how your tabs works).