You need to edit the link which you wish to have its own leftnav menus and select the option in link manager to Page starts new side navigation links and save.

Note : You cannot revert the changes back, i.e, You can change from "Page shows the same side navigation links as the parent page" to "Page starts new side navigation links" but not vice-versa

And this option is not available for pages created from the editor and only for pages created from the navigational menus (top/left)