The purpose of this study is to find out about the safety and how well the study intervention (elafibranor) works in participants with PBC. The participants in this study will have confirmed PBC with inadequate response or intolerance to UDCA, which is a medication used in the management and treatment of cholestatic liver disease. PBC is a slowly progressive disease characterised by damage of the bile ducts in the liver, leading to a build-up of bile acids which causes further damage. The liver damage in PBC may lead to scarring (cirrhosis). PBC may also be associated with multiple symptoms. Many patients with PBC may require a liver transplant or may die if the disease progresses and a liver transplant is not done. In this study all participants will receive a daily dose of elafibranor (the study intervention). The main aim of this study is to determine if elafibranor reduces alkaline phosphatase (ALP) and total bilirubin levels. High ALP and bilirubin levels in the blood can indicate liver disease. There will be 4 periods in this study: A screening period (up to 10 weeks) to assess whether the participant can take part. A treatment period (52 weeks) where all eligible participants will receive elafibranor. A variable treatment extension period (2-5 years) from completion of 52 week treatment period up to the commercial availability of elafibranor in Japan. A follow-up period (4 weeks) where participants’ health will be monitored. Participants will undergo blood sampling, urine collections, physical examinations, clinical evaluations, electrocardiograms (ECG: recording of the electrical activity of heart), ultrasound examinations (a non invasive test that passes a probe over skin to look at the bladder, urinary tract, and liver), and Fibroscan® examinations (to measure stiffness of the liver). They will also be asked to fill in questionnaires. Each participant will be in this study for up to approximately 6 years.