Inclusion Criteria:  For inclusion in the study, patient should fulfill the following criteria:  Female patient ≥ 18 years of age. Signed informed consent and ability to comply with treatment and follow-up.  Patient with newly diagnosed, a. Ovarian cancer, primary peritoneal cancer and/or fallopian-tube cancer, b. Histologically confirmed (based on local histopathological findings):  • high grade serous or  high grade endometrioid (grade 2 and 3) or other epithelial non mucinous and non-clear cell ovarian cancer in a patient with germline BRCA 1 or 2 deleterious mutation, c. At an advanced stage: FIGO stage IIIA to IIIC of the 2018 FIGO classification. Patient having undergone frontline, complete cytoreductive surgery (i.e. no visible residual disease): The patient will be considered eligible once the ESGO Quality Assurance in Ovarian Cancer Surgery will have been filled out and validated Eastern Cooperative Oncology Group (ECOG) performance status 0-1. Patient must have received one cycle of carboplatin AUC 5-6 + paclitaxel 175 mg/m² Patient must have started cycle 1 chemotherapy no later than 6 weeks after surgery. Patient must have a thorax-abdomen-pelvis CT scan between surgery and Cycle 1, with no evidence of disease. Patient eligible for first line platinum-taxane chemotherapy: Patient eligible for bevacizumab treatment in combination with chemotherapy and in maintenance. It must be started at the second chemotherapy cycle and be administered at a dose of 15mg/kg every 3 weeks up to a total of 15 months.  Patient must have normal organ and bone marrow function before first cycle of chemotherapy:  Hemoglobin ≥ 9.0 g/dL. Absolute neutrophil count (ANC) ≥ 1.5 x 109/L. Platelet count ≥ 100 x 109/L. Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN). Aspartate aminotransferase/Serum Glutamic Oxaloacetic Transaminase (ASAT/SGOT)) and Alanine aminotransferase /Serum Glutamic Pyruvate Transaminase (ALAT/SGPT)) ≤ 2.5 x ULN. Serum creatinine ≤ 1. 5 x institutional ULN and GFR > 50 mL/min, by using an exact measure (ie. Iohexol clearance) or the most appropriate formula (Jeliffe, Cockroft Gault, MDRD, CKD-EPI) to the investigator's discretion. Patient not receiving anticoagulant medication who has an International Normalized Ratio (INR) ≥1.5 and an Activated ProThrombin Time (aPTT) ≥1.5 x ULN.  The use of full-dose oral or parenteral anticoagulants is permitted as long as the INR or APTT is within therapeutic limits (according to site medical standard). If the patient is on oral anticoagulants, dose has to be stable for at least two weeks at the time of randomization.  Urine dipstick for proteinuria < 2+. If urine dipstick is ≥2+, 24-hour proteinuria must be <1 g. Normal blood pressure or adequately treated and controlled hypertension (systolic BP ≤ 140 mmHg and/or diastolic BP ≤ 90 mmHg). Formalin fixed paraffin embedded (FFPE) tumor sample from the primary cancer must be available for local BRCA testing and if possible HRD testing (optional). For countries where this will apply to: a subject will be eligible for randomization in this study only if either affiliated to, or a beneficiary of a social security category.  Exclusion Criteria:  1. Patient with clear cell adenocarcinoma or carcinosarcoma, non-epithelial origin of the ovarian tumor, the fallopian tube or the peritoneal tumor (i.e. germ cell tumors).  2. Ovarian tumor of low malignant potential (e.g. borderline tumor), or mucinous carcinoma.  3. Patient with a diagnosis, detection, or treatment of another type of cancer ≤ 3 years prior to initiating protocol therapy (except basal or squamous cell carcinoma of the skin and cervical cancer in situ that has been definitively treated and synchronous grade 1 stage 1 endometrial cancer) Patient with history of primary triple negative breast cancer may be eligible provided she completed her definitive anticancer treatment more than 3 years ago and she remains breast cancer disease free prior to start of study treatment.  4. Patient with synchronous high grade serous or clear cell adenocarcinoma or carcinosarcoma of the endometrium is not eligible.  5. Patient with myelodysplastic syndrome/acute myeloid leukemia history. 6. Patient receiving radiotherapy within 6 weeks prior to study treatment. 7. Previous allogenic bone marrow transplant. 8. Any previous treatment with PARP inhibitor. 9. Administration of other simultaneous chemotherapy drugs - except during a HIPEC procedure with cisplatin at PDS, any other anticancer therapy or anti-neoplastic hormonal therapy, or simultaneous radiotherapy during the trial treatment period (hormonal replacement therapy is permitted as are steroid antiemetics).  10. Current or recent (within 10 days prior to randomization) chronic use of aspirin > 325 mg/day.  11. Prior history of hypertensive crisis (CTC-AE grade 4) or hypertensive encephalopathy.  12. Clinically significant (e.g. active) cardiovascular disease, including:  Myocardial infarction or unstable angina within ≤ 6 months of randomization, New York Heart Association (NYHA) ≥ grade 2 congestive heart failure (CHF), Poorly controlled cardiac arrhythmia despite medication (patient with rate controlled atrial fibrillation are eligible), or any clinically significant abnormal finding on resting ECG.  Peripheral vascular disease grade ≥ 3 (e.g. symptomatic and interfering with activities of daily living [ADL] requiring repair or revision).  13. Previous Cerebro-Vascular Accident (CVA), Transient Ischemic Attack (TIA), Sub- Arachnoids Hemorrhage (SAH) or Posterior Reversible Encephalopathy Syndrome (PRES).  14. History or evidence of hemorrhagic disorders. 15. Evidence of bleeding diathesis or significant coagulopathy (in the absence of coagulation).  16. History or clinical suspicion of brain metastases or spinal cord compression. CT/MRI of the brain is mandatory (within 4 weeks prior to randomization) in case of suspected brain metastases. Spinal MRI is mandatory (within 4 weeks prior to randomization) in case of suspected spinal cord compression.  17. History or evidence upon neurological examination of central nervous system (CNS) disease, unless adequately treated with standard medical therapy (e.g. uncontrolled seizures).  18. Significant traumatic injury during 4 weeks prior to randomization. 19. Non-healing wound, active ulcer, or bone fracture. Patient with granulating incisions healing by secondary intention with no evidence of facial dehiscence or infection is eligible but require 3 weekly wound examinations.  20. History of VEGF therapy related abdominal fistula or gastrointestinal perforation or active gastrointestinal bleeding within 6 months prior to the first study treatment.  21. Current, clinically relevant bowel obstruction, including sub-occlusive disease, related to underlying disease.  22. Patient with evidence of abdominal free air not explained by paracentesis or recent surgical procedure.  23. Evidence of any other disease, metabolic dysfunction, physical examination finding or laboratory finding giving reasonable suspicion of a disease or condition that contraindicates the use of an investigational drug or puts the patient at high risk for treatment related complications.  24. Pregnant or lactating women. 25. Participation in another clinical study with any intravenous or oral investigational product is not allowed. However, participation in a surgical clinical study including Hyperthermic Chemotherapy (HIPEC) during the surgical procedure is allowed.  26. Patient unable to swallow orally administered medication and patient with gastrointestinal disorders likely to interfere with absorption of the study medication.  27. Patient with a known contraindication or uncontrolled hypersensitivity to the components of paclitaxel, carboplatin, niraparib, bevacizumab, or their excipients.  28. Immunocompromised patient, e.g., with known active hepatitis (i.e. Hepatitis B or C) due to risk of transmitting the infection through blood or other body fluids or patient who is known to be serologically positive for human immunodeficiency virus (HIV).  29. Participant has a serious, uncontrolled medical disorder, nonmalignant systemic disease, or active, uncontrolled infection. Examples include, but are not limited to uncontrolled major seizure disorder, unstable spinal cord compression, superior vena cava syndrome, or any psychiatric disorder that prohibits obtaining informed consent.