gio:menu-item-set-submenu (item submenu)

item -- a g:menu-item object
submenu -- a g:menu-model object, or nil

Sets or unsets the "submenu" link of the menu item to submenu. If submenu is not nil, it is linked to. If it is nil then the link is unset.

The effect of having one menu appear as a submenu of another is exactly as it sounds.