Objective To determine what issues are experienced during the first few weeks of therapy by patients, and their parents/carers, when a child/young person has been prescribed a new medicine. Method One hundred patients aged ≤18 years of age prescribed a new medicine for ≥6 weeks were recruited from a single UK National Health Service specialist paediatric hospital outpatient pharmacy. Six weeks after the first dispensing of their new medicine the patient or their parent/carer received telephone follow-up by a researcher and verbally completed a questionnaire containing both open and closed questions. Patient or parent/carer experiences were identified and analysed using thematic analysis and descriptive statistics. Results Eighty-six participants were available for telephone follow-up. Six (7%) had not started their medicine. Paediatric patients and their parents/carers experienced a range of issues during the first few weeks after starting a new medicine. These included additional concerns/questions (24/80, 30%), administration issues (21/80, 26.3%), adverse effects (29/80, 36.3%) and obtaining repeat supplies (12/80, 15%). The Morisky Medication Adherence Scale indicated that 34/78 (43.6%) participants had a high adherence rating, 35/78 (44.9%) medium and 9/78 (11.5%) a low rating. Conclusions Paediatric patients and their parents/ carers experience a range of issues during the first few weeks after starting a new medicine. Further research is required to determine the type of interventions that may further support medicines use in this group of patients.