Dr. Clark worked at the hospital where Arthur Ketch was taken for treatment after being shot by Dean Winchester. She was presumably his doctor.
In order to get close to Arthur, the demonArdat takes Dr. Clark as her vessel. As Arthur tries to leave, a nurse finds Ardat behind her and is pleased to see the demon, mistaking her for Dr. Clark. Ardat then kills the nurse and Arthur and continues to use Dr. Clark as her vessel.