Newly Diagnosed Stage III/IV Ovarian Cancer, Neoadjuvant Carbo/Taxol/Pembro, Maintenance Olaparib/Pembro

Inclusion Criteria: * Participants are eligible to be included in the study only if all of the following criteria apply: 1. Participant has histologically confirmed FIGO Stage III or Stage IV EOC (high-grade predominantly serous, endometrioid, carcinosarcoma, mixed Mullerian with high grade serous component, clear cell, or low-grade serous OC), primary peritoneal cancer, or fallopian tube cancer. 2. Participant is a candidate for carboplatin and paclitaxel chemotherapy, to be administered in the neoadjuvant setting with planned interval debulking surgery. 3. Participant that is a candidate for neoadjuvant chemotherapy has a CA-125 (kilounits/L) : carcinoembryonic antigen (CEA; ng/mL) ratio greater than or equal to 25 \[Vergote, I., et al 2010\]. Note: if the serum CA-125/CEA ratio is less than 25, then a workup should be negative for the presence of a non-ovarian cancer to determine eligibility (e.g., breast or gastrointestinal cancers \[including CRC\]). 5\. Participant is female and at least 18 years of age on the day of signing informed consent. 6\. Participant has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1, as assessed within 7 days prior to enrollment. 7\. A female participant is eligible to participate if she is not pregnant, not breastfeeding, and at least 1 of the following conditions applies: a.) Not a woman of childbearing potential (WOCBP) OR b.) A WOCBP who agrees to follow contraceptive guidance during the Treatment Period and for at least 120 days following the last dose of pembrolizumab and olaparib and at least 210 days following the last dose of chemotherapy 8. The participant (or legally acceptable representative if applicable) provides written informed consent for the study. The participant may also provide consent for future biomedical research; however, the participant may participate in the main study without participating in future biomedical research. 9\. Participant has adequate organ function as follows; all screening laboratory tests should be performed within 7 days of enrollment: 1. Absolute neutrophil count (ANC) ≥1500/μL 2. Platelets ≥100 000/μL 3. Hemoglobin ≥8.0 g/dL or ≥5.6 mmol/L 4. Creatinine OR measured or calculated creatinine clearance (GFR can also be used in place of creatinine or CrCl) ≤1.5 × ULN OR ≥51 mL/min for participant with creatinine levels \>1.5 × institutional ULN 5. Total bilirubin ≤1.5 ×ULN OR direct bilirubin ≤ULN for participants with total bilirubin levels \>1.5 × ULN 6. AST (SGOT) and ALT (SGPT) ≤2.5 × ULN (≤5 × ULN for participants with liver metastases) 7. International normalized ratio (INR) OR prothrombin time (PT); Activated partial thromboplastin time (aPTT) or partial thromboplastin time (PTT) ≤1.5 × ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants Exclusion Criteria: * Participants are excluded from the study if any of the following criteria apply: 1. Participant has mucinous, germ cell, or borderline tumor of the ovary. 2. Participant has a history of non-infectious pneumonitis that required treatment with steroids or currently has pneumonitis. 3. Participant either has myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML) or has features suggestive of MDS/AML. 4. Participant has a known additional malignancy that is progressing or has required active treatment in the last 3 years. Note: Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or carcinoma in situ (e.g., ductal carcinoma in situ, cervical carcinoma in situ) that has undergone potentially curative therapy are not excluded. Additionally, participants with synchronous primary endometrial cancer or a past history of primary endometrial cancer that met the following conditions are not excluded: Stage not greater than I-A; no more than superficial myometrial invasion, without vascular or lymphatic invasion; no poorly differentiated subtypes, including papillary serous, clear cell or other FIGO Grade 3 lesions. 5. Participant has known active central nervous system metastases and/or carcinomatous meningitis. Participants with brain metastases may participate provided they were previously treated (except with chemotherapy) and are radiologically stable, clinically stable, and no steroids were used for the management of symptoms related to brain metastases within 14 days prior to enrollment. Stable brain metastases should be established prior to the first dose of study medication. Note: Participants with known untreated, asymptomatic brain metastases (i.e., no neurological symptoms, no requirement for corticosteroids, no or minimal surrounding edema, and no lesion \>1.5 cm) may participate but will require regular imaging of the brain as a site of disease. 6. Participant has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (dosing exceeding 10 mg dailyof prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to enrollment. 7. Participant has an active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease modifying agents, corticosteroids, or immunosuppressive drugs). Note: Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment and is allowed. 8. Participant has a known history of active tuberculosis (TB; Bacillus Tuberculosis). 9. Participant has an active infection requiring systemic therapy. 10. Participant is considered to be of poor medical risk due to a serious, uncontrolled medical disorder, non-malignant systemic disease or active, uncontrolled infection. 11. Participant has had surgery to treat borderline tumors, early stage EOC, or fallopian tube cancer \<6 months prior to screening. 12. Participant has a known psychiatric or substance abuse disorder that would interfere with the ability to cooperate with the requirements of the study. 13. Participant has a known history of human immunodeficiency virus (HIV) infection. 14. Participant has a known history of hepatitis B (defined as hepatitis B surface antigen \[HBsag\] reactive) or known active hepatitis C virus (defined as HCV RNA \[qualitative\] is detected) infection. 15. Participant has received prior treatment for advanced or metastatic OC, including radiation or systemic anti-cancer therapy (e.g., chemotherapy, hormonal therapy, immunotherapy, investigational therapy). 16. Participant has severe hypersensitivity (≥Grade 3) to pembrolizumab, olaparib, carboplatin, or paclitaxel, and/or any of their excipients. 17. Participant has resting electrocardiogram (ECG) indicating uncontrolled, potentially reversible cardiac conditions, as judged by the investigator (e.g., unstable ischemia, uncontrolled symptomatic arrhythmia, congestive heart failure, QTcF prolongation\>500 ms, electrolyte disturbances, etc.), or participant has congenital long QT syndrome. 18. Participant has had an allogenic tissue/solid organ transplant, has received previous allogenic bone-marrow transplant, or has received double umbilical cord transplantation. 19. Participant has received prior therapy with olaparib or with any other PARP inhibitor. 20. Participant has a known hypersensitivity to the components or excipients in olaparib. 21. Participant is currently receiving either strong (e.g., itraconazole, telithromycin, clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir) or moderate (e.g. ciprofloxacin, erythromycin, diltiazem, fluconazole, verapamil) inhibitors of cytochrome P450 (CYP)3A4 that cannot be discontinued for the duration of the study. The required washout period prior to starting olaparib is 2 weeks. 22. Participant is currently receiving either strong (phenobarbital, enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine and St John's Wort) or moderate (e.g. bosentan, efavirenz, modafinil) inducers of CYP3A4 that cannot be discontinued for the duration of the study. The required washout period prior to starting olaparib is 5 weeks for phenobarbital and 3 weeks for other agents. Note: a current list of strong/moderate inducers of CYP3A4 can be found at the following website: https://www.fda.gov/drugs/drug-interactions-labeling/drug-development-and-drug-interactions-table-substrates-inhibitors-and-inducers 23. Participant has received a whole blood transfusion in the last 120 days prior to entry to the study. Packed red blood cells and platelet transfusions are acceptable if not performed within 28 days of the first dose of study intervention. Participant received colony-stimulating factors (e.g., granulocyte colony-stimulating factor \[G-CSF\], granulocyte-macrophage colony-stimulating factor \[GM CSF\] or recombinant erythropoietin) within 28 days prior to the first dose of study intervention. 24. Participant is unable to swallow orally administered medication or has a gastrointestinal disorder affecting absorption (e.g., gastrectomy, partial bowel obstruction, malabsorption). 25. Participant is considered a poor medical risk due to a serious, uncontrolled medical disorder, non-malignant systemic disease or active, uncontrolled infection. Examples include, but are not limited to, uncontrolled ventricular arrhythmia, recent (within 3 months) myocardial infarction, uncontrolled major seizure disorder, unstable spinal cord compression, superior vena cava syndrome, extensive interstitial bilateral lung disease on High Resolution Computed Tomography (HRCT) scan or any psychiatric disorder that prohibits obtaining informed consent. 26. Participant has uncontrolled hypertension, defined as defined as systolic \>140 mm Hg or diastolic \>90 mm Hg documented by 2 blood pressure readings taken at least 1 hour apart. Note: This applies to participants who will receive bevacizumab. 27. Use of antihypertensive medications to control blood pressure is allowed. Participant has current, clinically relevant bowel obstruction (including sub-occlusive disease), abdominal fistula or gastrointestinal perforation, related to underlying EOC. Note: This applies to participants who will receive bevacizumab. 28. Participant has a history of hemorrhage, hemoptysis or active gastrointestinal bleeding within 6 months prior to enrollment Note: This applies only to participants who will receive bevacizumab. 29. Participant is currently participating or has participated in a study of an investigational agent or has used an investigational device within 4 weeks of the first dose of study treatment. 30. Participant, in the judgement of the investigator, is unlikely to comply with the study procedures, restrictions, and requirements of the study.