In this Phase II trial the efficacy of treatment in patients with clinically significant portal hypertension (CSPH), in compensated alcohol-related cirrhosis, will be assessed. This will be the first trial in the clinical development of the drug BI 685509 where patients will be treated for 24 weeks, and where the portal pressure will be assessed quantitatively via HVPG measurements. The trial will evaluate both short-term and long-term efficacy. The long-term assessment will be used to rule out any adaptation to sGC activation on portal pressure on chronic treatment. The trial will also provide supportive evidence for the planned Phase III development.