Key Inclusion Criteria:  1,Participants must be ≥18 years at the time of (pre-)screening  2,Histological and staging criteria:Female participants who must have histologically newly diagnosed high-grade serous or endometrioid ovarian cancer, fallopian tube cancer, or primary peritoneal cancer that is Stage III or IV according to the International FIGO 2009.  3, Participants are eligible if they fulfil any of the following surgical criteria:  Stage III: primary debulking surgery with macroscopic residual disease post-surgery, neoadjuvant chemotherapy, or inoperable.  Stage IV: primary debulking surgery regardless of residual disease, neoadjuvant chemotherapy, or inoperable.  4, Chemotherapy criteria:  Participants must have received platinum-based chemotherapy consisting of a minimum of 6 treatment cycles and a maximum of 9, however, if platinum-based therapy must be discontinued early as a result of toxicities specifically related to the platinum regimen, participants must have received a minimum of 4 cycles of the platinum regimen. Participants must have, in the opinion of the investigator, clinical CR or PR as per RECIST 1.1 criteria with no measurable lesion > 2 cm on the post-treatment scan and have no clinical evidence of disease progression or a rising CA-125 level (see inclusion criterion 5), following completion of this chemotherapy course.  A participant who received interval debulking surgery must have had ≥ 2 postoperative cycles of platinum-based therapy.  5, Participants must meet one of the criteria specified below for pre-treatment CA-125 measurements as follows:  CA-125 in the normal range or  CA-125 decrease by ≥ 90% during their front-line therapy that is stable for at least 7 days (ie, no increase > 15% from nadir. If the first value is greater than the upper limit of normal (ULN), a second assessment must be performed at least 7 days after the first. If the second assessment is > 15% more than the first value, the participant is not eligible).  6, Participants should not have received bevacizumab with first-line chemotherapy or be planned to receive bevacizumab maintenance therapy.  7, ECOG performance status of 0 or 1 with no deterioration over the previous 2 weeks prior to randomisation.  8, Provision, at pre-screening, of a formalin-fixed, paraffin-embedded (FFPE) tumour sample to assess tBRCA status and for HRD testing centrally. The centrally performed tBRCA test results must be available prior to randomisation and must indicate that the participant has a BRCAwt tumour, defined by the absence of a deleterious or suspected deleterious BRCA mutation by central testing.  9, Adequate organ and marrow function.  Key Exclusion Criteria:  1, Participants with stable disease or progressive disease on the post-treatment scan or clinical evidence of progression at the end of the participant's first-line chemotherapy treatment, or any evidence of progressive disease prior to randomization.  2, Participant has mucinous or clear cell subtypes of epithelial ovarian cancer, carcinosarcoma, undifferentiated ovarian cancer, non-epithelial ovarian cancer, borderline tumours or low grade epithelial ovarian tumours (applies to fallopian tube and primary peritoneal tumours where applicable).  3, Participants with Stage III disease who have had complete cytoreduction (ie, no macroscopic residual disease) at their primary debulking surgery.  4, Participants who have undergone ˃ 2 debulking (cytoreductive) surgeries.  5, History of another primary malignancy except for malignancy treated with curative intent with no known active disease ≥ 5 years before the first dose of study intervention including adequately treated non-melanoma skin cancer, curatively treated in situ cancer of the cervix, ductal carcinoma in situ (DCIS), Stage 1, Grade 1 endometrial carcinoma. Participants with a history of localised triple negative breast cancer may be eligible, provided they completed their adjuvant chemotherapy more than three years prior to registration, and that the participant remains free of recurrent or metastatic disease.  6, Persistent toxicities (CTCAE Grade ≥2) caused by previous anticancer therapy, excluding alopecia and CTCAE Grade 2 peripheral neuropathy. Participants with irreversible toxicity that is not reasonably expected to be exacerbated by study intervention may be included after consultation with the AstraZeneca study physician.  7, Participant is immunocompromised  8, Prior exposure to a PARP inhibitor, including olaparib  9, Any concurrent anticancer treatment  10, Currently pregnant or breast-feeding