You may work as an Audiologist, Speech Language Therapist , Speech Language Pathologist ,Rehabilitation specialist ,Hearing aids marketer, Hearing aids specialist, Instructor/Teacher (at special schools) or ngos.
Some well known employers/places where graduates may find job after completing BASLP course are-
Government and Private Hospitals (departments like Neurology, Paediatrics and ENT)Rehabilitation Clinics, Special Schools for Children suffering from hearing and speech disorders,NGOs, Hearing aids and implants manufacturing companies, Research firms etc.

Or in terms of education you can study masters degree in it.
Good luck.