Inclusion criteria:  Male patients who are at least 18 years of age on the day of signing informed consent Histologically confirmed diagnosis of an adenocarcinoma of the prostate and a BCR or PSA persistence after RP Histology of the RP specimen needs to fulfill the following criteria: adenocarcinoma of the prostate, Gleason score 7-10; pNX or pN0 or pN1 (max. 2 lymph nodes involved) Imaging within 30 days prior to study inclusion is mandatory (([68Ga] or [18F] PSMA PET-CT as standard imaging modality, alternatively CT abdomen and full-body bone scan) PSA value between ≥0.2 and ≤1.0 ng/ml measured at least six weeks postoperatively The patients agree not to undergo testicular sperm extraction for at least 90 days after the last administration of pembrolizumab. (Due to prior surgical removal of the prostate no contraception is necessary.) Written informed consent obtained according to international guidelines and local law Patients further having an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1. Patients with adequate organ function as defined in clinical trial protocol (CTP) (Section 4)  Exclusion criteria:  Prior-therapy with an anti-PD-1, anti-PD-L1, or anti PD L2 agent or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (e.g., CTLA-4, OX 40, CD137). Prior systemic anti-cancer therapy including investigational agents within 4 weeks prior to registration (like neo-adjuvant androgen deprivation therapy (ADT), secondary hormone ablation or taxan-based chemotherapy). Prior radiotherapy within 4 weeks before start of study medication. Patients must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. Distant metastases or suspicious lymph nodes outside the lower pelvis in imaging with PSMA PET-CT are to be excluded (patients with PET positive bone lesions that are morphologically not clearly suspicious of metastases and would not change clinical practice can be included). Adverse histology of RP specimen (e.g. neuroendocrine or small cell) Any vaccination with live vaccine or live-attenuated vaccine within 30 days prior to the first dose of study medication. Administration of killed vaccines is allowed. Currently or previously participating in a study of an investigational product within 4 weeks prior to the first dose of study medication. Diagnosis of immunodeficiency, chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study medication. History of a second malignancy, unless potentially curative treatment has been completed with no evidence of malignancy for 2 years. Known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Severe hypersensitivity (≥Grade 3) to pembrolizumab and/or any of its excipients. Active autoimmune disease that required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g. thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment and is allowed. History of (non-infectious) pneumonitis/interstitial lung disease that required steroids or currently pneumonitis/ interstitial lung disease Active infection requiring systemic therapy. History of Human Immunodeficiency Virus (HIV) infection. History of Hepatitis B (defined as Hepatitis B surface antigen [HBsAg] reactive) or known active Hepatitis C virus (defined as Hepatitis C virus (HCV) RNA is detected) infection. No testing is required. History of active TB (Bacillus Tuberculosis). History or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the subject to participate, in the opinion of the investigator. Known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. History of allogeneic tissue/solid organ transplantation.