Researchers are looking for a better way to treat men at high-risk of biochemical recurrence (BCR) of prostate cancer. BCR means that in men who had prostate cancer and were treated by either surgery and/ or radiation therapy, the blood level of a specific protein called PSA rises. PSA is a marker of prostate cancer cells activity. The PSA increase means that the cancer has come back even though conventional imaging such as computed tomography (CT) scans, magnetic resonance imaging (MRI) and bone scans does not show any lesion of prostate cancer. Recently a more sensitive imaging method called prostate-specific membrane antigen \[PSMA\] positron emission tomography \[PET\]) /computed tomography \[CT\]) scan may identify prostate cancer lesions not detectable by conventional imaging. Men with BCR have a higher risk of their cancer spreading to other parts of the body, particularly when PSA levels raised to a certain limit within a short period of time after local therapies. Once the cancer spreads to other parts of the body, it can become even harder to treat. In men with prostate cancer, male sex hormones (also called androgens) like testosterone can help the cancer grow and spread. To reduce androgens levels in these patients, there are treatments that block androgens production in the body called androgen deprivation therapy (ADT). ADT is often used to stop prostate cancer. Another way to stop prostate cancer growth and spread is to block the action of androgen receptors on prostate cancer cells called androgen receptor inhibitors (ARIs). The new generation ARIs including darolutamide can block the action of androgens receptors and are available for the treatment of prostate cancer in addition to ADT. It is already known that men with prostate cancer benefit from these treatments. The main objective of this study is to learn if the combination of darolutamide and ADT prolongs the time that the participants live without their cancer getting worse, or to death due to any cause, compared to placebo (which is a treatment that looks like a medicine but does not have any medicine in it) and ADT given for a pre-specified duration of 24 months. To do this, the study team will measure the time from the date of treatment allocation to the finding of new cancer spread in the participants by using PSMA PET/CT, or death due to any cause. The PSMA PET/CT scans is performed using a radioactive substance called a tracer that specifically binds to the prostate-specific membrane antigen (PSMA) which is a protein often found in large amounts on prostate cancer cells. To avoid bias in treatment, the study participants will be randomly (by chance) allocated to one of two treatment groups. Based on the allocated treatment group, the participants will either take darolutamide plus ADT or placebo plus ADT twice daily as tablets by mouth. The study will consist of a test (screening) phase, a treatment phase and a follow-up phase. The treatment duration is pre-specified to be 24 months unless the cancer gets worse, the participants have medical problems, or they leave the study for any reason. In addition, image guided radiotherapy (IGRT) or surgery is allowed and your doctor will explain the benefits and risks of this type of therapy. During the study, the study team will: * take blood and urine samples. * measure PSA and testosterone levels in the blood samples * do physical examinations * check the participants' overall health * examine heart health using electrocardiogram (ECG) * check vital signs * check cancer status using PSMA PET/CT scans, CT, MRI and bone scans * take tumor samples (if required) * ask the participants if they have medical problems About 30 days after the participants have taken their last treatment, the study doctors and their team will check the participants' health and if their cancer worsened. The study team will continue to check this and regularly ask the participants questions about medical problems and subsequent therapies until they leave the study for any reason or until they leave the study for any reason or until the end of the study, whatever comes first.