Osteogenesis imperfecta (OI) is an inherited skeletal disorder characterised by increased risk of fragility fractures. Bisphosphonates are frequently prescribed for adult patients with OI with the aim of preventing fractures but the evidence base for efficacy is poor. Recent evidence suggests that the bone anabolic agent teriparatide (TPTD) increases bone mineral density (BMD) and may have the potential to prevent fractures in OI. The purpose of the TOPaZ Trial is to investigate if a a two-year course of teriparatide (TPTD) followed by antiresorptive therapy with a single infusion of zoledronic acid (ZA) in adults with OI reduces the proportion of patients who experience a fracture as compared with standard care Adult patients with a clinical diagnosis of OI who are willing and able to give informed consent and who do not have contraindications to the study medications will be recruited from participating sites. Participants will be randomised 1:1 to receive either standard care for the duration of the trial or TPTD for 24 months followed by a single infusion of ZA, or another antiresorptive agent in the event that ZA is contraindicated. Participants will attend recruiting centres for a Baseline/Screening visit, at 12 months, 24 months and at the end of the trial for formal study visits with telephone calls every 6 months from a site research nurse. Participants randomised to TPTD will also attend recruiting centre at regular intervals during the 24 month treatment period to collect new supplies of TPTD.