This depends on how you decide to panel your stairs and hallway. If simply adding moulding directly to the wall, you can leave the skirting board in place. But you may want a different skirting board idea to replace the current skirting board and match your moulding.
If you are installing panels first we recommend that you remove the skirting board to get a professional looking finish. You can add new skirting board on top of the panels before adding your moulding and painting.