fill (one's) prescription
1. To supply and sell a dose or set of doses of a medicine as prescribed to one by a doctor. Because of the strength of the medication, I have to be there in person with ID when they fill my prescription for the first time. When filling a patient's prescription, you have to be sure that all directions and warnings are on the medicine and said to the patient directly.
2. To go to or contact a pharmacy in order to buy a dose or set of doses of a medicine as prescribed by a doctor. Do you mind if we swing by the pharmacy on the way home? I need to fill my new prescription. She just went in to fill her prescription—she should be back in a minute.