Object Permissions
You know that writing some text in your question is free? Things like ... a version (as you said product is OBIEE) always helps. Then qualifying things a bit, like what do you call a "tab"? What kind of object is that? Is that a dashboard subpage?
And if you express this you also find your answer half of the time: if the "tab" is a dashboard subpage, it just behave like any other page in any dashboard, with permissions on it.
The "permissions" icon (the key) does not appear, even though we are the admin user. What privilege do I have to have for it to appear?
the image is from another co-worker
regards
If the "key icon" doesn't appear it maybe means you don't have the permission "change permission" on that object.
Being an admin doesn't mean you have full access to everything, the catalog objects have permissions applying to everybody, admins included.