Currently in the Kanban Board, if you have a sub-task that is in a different column from its parent issue, there is a gray ribbon above the subtask indicating its parent issue key and summary.
This can be very tedious to view when the Kanban backlog gets bigger, since its difficult to refer to a subtask's parent issue. This gray ribbon should also act as a link that automatically selects the parent issue in the board.

Note that this is not accounting the STORIES swimlane as some users prefer not using any swimlanes to keep the Kanban board compact.