A Study to Learn How Safe AZD6621 is, How Well it Works, and How it Moves Throughout the Body Over Time, in Adult Male Participants With Metastatic Prostate Cancer

Inclusion Criteria 1. Capable of giving signed informed consent and complying to the study protocol. 2. Provision of signed and dated written Optional Genomics Initiative Research Information and Consent Form. 3. ≥ 18 years of age at the time of signing the informed consent form. 4. Participants with: 1. Histologically confirmed diagnosis of metastatic adenocarcinoma of the prostate 2. Surgically or medically castrated, with serum testosterone levels ≤ 50 ng/dL (≤ 1.75 nmol/L) ≤ 28 days before first dose of study intervention. Participants without prior surgical castration must be currently taking and willing to continue LHRH agonist or antagonist therapy throughout the duration of the study intervention. 3. Castration-resistant prostate cancer as defined by disease progression despite castration by orchiectomy or ongoing ADT. 4. PSA at screening visit ≥ 1 ng/mL. 5. Provision of baseline fresh or archival tumor biopsy of prostate carcinoma is mandatory. 6. Evidence of disease progression within 6 months prior to screening with at least one of the following: 1. PSA progression defined by a minimum of 3 rising PSA levels with an interval of ≥ 1 week between each determination. 2. Radiographic progression of soft tissue disease by RECIST v1.1 criteria with or without PSA progression. 3. Radiographic progression of bone metastasis by PCWG3 criteria with 2 or more documented new bone lesions on a bone scan with or without PSA progression. 7. Part A: Module 1 and Module 2: 1. Part A: Module 1 and Module 2 prior anti-cancer treatment requirements as stated in study protocol 2. Pharmacodynamic backfill cohort(s) only: lesion amenable for biopsy and be willing to undergo biopsy, distinct from any target lesion used in the RECIST v1.1 evaluation, unless there are no other lesions available for biopsy. 8. Part B: Module 1 and Module 2: 1. Part B: Module 1 and Module 2 prior anti-cancer treatment requirements as stated in study protocol. 2. Participants may have received PARP inhibitors or checkpoint inhibitors per local treatment guidelines. 3. Sampling Requirements as stated in study protocol. 9. ECOG PS score of 0 or 1. 10. Minimum life expectancy of \> 12 weeks. 11. Adequate hematological, renal, bone marrow, and liver function as documented in the protocol. 12. Body weight ≥ 35 kg. 13. Male, as assigned at birth, inclusive of all gender identities. 14. Contraceptive use by participants or participant partners as documented in the protocol and consistent with local regulations. Exclusion Criteria 1. Any evidence of diseases (such as severe or uncontrolled systemic diseases) which in the Investigator's opinion makes it undesirable for the participant to participate in the study. 2. One or more of the following: 1. Mean resting corrected QT interval \> 470 ms, 2. History of QT prolongation associated with other medications that required discontinuation of that medication, or any current concomitant medication known to prolong the QT interval and cause Torsades de Pointes. 3. Congenital long QT syndrome, family history of long QT syndrome, or unexplained sudden death under 40 years of age in first degree relatives. 4. Inadequate cardiac function of LVEF \< 50% on screening cardiac MUGA or ECHO. 3. Cardiac arrhythmias (such as multifocal premature ventricular contractions, bigeminy, trigeminy, ventricular tachycardia), which are symptomatic or require treatment unless controlled by pacemaker; symptomatic or uncontrolled atrial fibrillation despite treatment, or asymptomatic sustained ventricular tachycardia. 4. History of another primary malignancy except for malignancy treated with curative intent with no known active disease (≥ 2 years) before the first dose of study intervention and of low potential risk for recurrence. 5. History of, or planned organ or allogeneic stem cell transplantation. 6. Unresolved toxicity from prior anti-cancer therapy of CTCAE Grade ≥ 2 (exceptions listed in protocol). 7. History of Grade ≥ 3 CRS or Grade ≥ 2 ICANS based on ASTCT criteria with prior therapy. CRS must be resolved prior to screening. 8. Previous history of hemophagocytic lymphohistiocytosis/ macrophage activation syndrome. 9. Active or prior documented autoimmune or inflammatory disorders (examples in protocol) within the past 3 years prior to the start of treatment or requiring permanent immunosuppressive therapy. 10. Spinal cord compression unless asymptomatic and treated and stable and not requiring continuous corticosteroids at a dose of \> 10 mg prednisone/day or equivalent. 11. CNS pathology (examples in protocol). 12. Active or uncontrolled hepatitis B or C virus infection (exceptions listed in the protocol). 13. Known HIV infection that is not well controlled (definition for HIV infection that is well controlled is listed in protocol). 14. Radiation therapy within 4 weeks of first dose of study intervention (or local or focal radiotherapy within 2 weeks of first dose). 15. Prior anti-cancer drug exposure requirement as stated in study protocol 16. Previous anti-cancer treatment requirements as stated in study protocol 17. Systemic corticosteroids at doses exceeding 10 mg/day of prednisone or equivalent \< 7 days prior to first dose. 18. Major surgical procedure or significant traumatic injury within 4 weeks prior to first dose. 19. Receipt of the last dose of anti-cancer therapy or participation in another clinical study with last dose administered in the last 21 days or 5 half-lives, whichever is shorter \- CAR-T cell therapy within the last 6 months prior to enrolment on this study. 20. Participants with a known hypersensitivity to AZD6621 or any of its excipients. 21. Involvement in the planning and/or conduct of the study. 22. Participant is unlikely to comply with study procedures, restrictions, and requirements (as judged by the Investigator). 23. Receipt of live attenuated vaccine within 30 days prior to the first dose of study in