It depends. Do you want the user to be aware that the action is possible, just not for them? In that case, show them the button, but disable it. An example might be if a user doesn't have delete authority, but other users do, they should know that entries CAN be deleted, so they can ask someone to do it for them if they need the action.
On the other hand, if the user is not supposed to even know about the action (for example, a user who does not have read access to audit logs probably shouldn't know that these logs exist) should not be able to see the button, so hide it completely.
