If you don't see an Admin tab on your club page, it's almost always down to your role in that specific club.
Your role is club-specific
PLAI checks your role separately for every club you're part of. You could be a Full Admin of one club and just a Member of another, so the tabs you see change depending on which club you're viewing.
Full Admins and Group Admins see the Admin tab, along with management tools scoped to their level of access.
Members don't see the Admin tab at all. Your club page opens on the Comms tab instead.
If you think this is wrong
If you believe you should have admin access, contact one of your club's existing Full Admins. Only they can promote you, see "How to Add, Assign, and Remove Club Admins."
FAQ
I'm an admin of one club but not another, is that normal?
Yes. Admin access is granted per club, not account-wide. Switching between clubs you belong to can change what you see.