• Duration of Response (DOR) [ Time Frame: Up to 5 years ]
  DOR is defined as the time from first documentation of response (CR or PR) until the time of first documentation of disease progression by RECIST v.1.1 based on Investigator assessment or death by any cause in the absence of progression by RECIST v.1.1.
• Progression-free Survival (PFS) [ Time Frame: Up to 5 years ]
  PFS is defined as the time from the date of the first dose of study treatment to the earlier date of assessment of progression by RECIST v.1.1 based on Investigator assessment or death by any cause in the absence of progression by RECIST v.1.1.
• Overall Survival (OS) [ Time Frame: Up to 5 years ]
  OS is defined as the time from the date of the first dose of study treatment to the date of death by any cause.
• Disease Control Rate (DCR) [ Time Frame: Up to 5 years ]
  DCR is defined as the percentage of patients who have achieved best overall response (BOR) of CR, PR, or stable disease (SD) per RECIST v.1.1 based on the Investigator's assessment.
• ORR Based on Independent Review Committee Assessment [ Time Frame: Up to 5 years ]
  ORR based on independent review committee assessment is defined as the percentage of participants who have achieved confirmed CR or PR per RECIST v1.1 based on the independent review committee assessment.
• DOR based on Independent Review Committee Assessment [ Time Frame: Up to 5 years ]
  DOR is defined as the time from first documentation of response (CR or PR) until the time of first documentation of disease progression by RECIST v.1.1 based on Independent Review Committee Assessment or death by any cause in the absence of progression by RECIST v.1.1.
• PFS based on Independent Review Committee Assessment [ Time Frame: Up to 5 years ]
  PFS is defined as the time from the date of the first dose of study treatment to the earlier date of assessment of progression by RECIST v.1.1 based on Independent Review Committee Assessment or death by any cause in the absence of progression by RECIST v.1.1.
• DCR based on Independent Review Committee Assessment [ Time Frame: Up to 5 years ]
  DCR is defined as the percentage of participants who have achieved BOR of CR, PR, or SD per RECIST v.1.1 based on Independent Review Committee Assessment.

• Duration of Response (DOR) [ Time Frame: Up to 5 years ]
  DOR is defined as the time from first documentation of response (CR or PR) until the time of first documentation of disease progression by RECIST v.1.1 based on Investigator assessment or death by any cause in the absence of progression by RECIST v.1.1.
• Progression-free Survival (PFS) [ Time Frame: Up to 5 years ]
  PFS is defined as the time from the date of the first dose of study treatment to the earlier date of assessment of progression by RECIST v.1.1 based on Investigator assessment or death by any cause in the absence of progression by RECIST v.1.1.
• Overall Survival (OS) [ Time Frame: Up to 5 years ]
  OS is defined as the time from the date of the first dose of study treatment to the date of death by any cause.
• Disease Control Rate (DCR) [ Time Frame: Up to 5 years ]
  DCR is defined as the percentage of patients who have achieved best overall response (BOR) of CR, PR, or SD per RECIST v.1.1 based on the Investigator's assessment.
• Objective Response Rate Based on Independent Review Committee Assessment [ Time Frame: Up to 5 years ]
  ORR based on independent review committee assessment is defined as the percentage of patients who have achieved confirmed CR or PR per RECIST v1.1 based on the independent review committee assessment.

• Drug: Niraparib
  Niraparib is a potent, orally active poly (adenosine diphosphate-ribose) polymerase (PARP)-1 and PARP2 inhibitor being developed as a treatment for participants with tumors that harbor defects in the homologous recombination deoxyribonucleic acid (DNA) repair pathway or that are driven by PARP-mediated transcription factors.
  Other Name: ZEJULA
• Drug: TSR-042
  TSR-042 is a humanized monoclonal antibody that binds with high affinity to programmed cell death-1 (PD-1) resulting in inhibition of binding to programmed cell-death receptor ligands 1 and 2 (PD-L1 and PD-L2).
  Other Name: Dostarlimab

Inclusion criteria:

• Participant must be female >=18 years of age, able to understand the study procedures, and subsequently agreed to participate in the study by providing written informed consent.
• Participants must have recurrent high-grade serous, endometrioid, or clear cell ovarian, fallopian tube, or primary peritoneal cancer.
• Participants must be considered resistant to the last administered platinum therapy.
• Participants must have completed at least 1 but no more than 3 prior lines of therapy for advanced or metastatic ovarian cancer.
• Participants must have been previously treated with platinum-based regimen, taxane agent(s), and bevacizumab.
• Participant has measurable disease according to RECIST v.1.1.
• Participant has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.
• Participant has adequate organ function.
• Females with childbearing potential have a serum pregnancy test that is negative 72 prior first dose and are not breastfeeding. Participant must also agree to abstain from activities that could result in pregnancy from enrollment through 180 days after the last dose of study treatment.
• Participant must provide formalin fixed paraffin embedded (FFPE) tumor tissue block(s) with sufficient tumor content (as confirmed by the Sponsor's designated central laboratory) during screening to enable BRCA testing and PD-L1 testing. Slides cut from FFPE blocks are not acceptable.
• Participant must agree to complete health-related quality of life (HRQoL) questionnaires throughout the study.

Exclusion Criteria:

• Participant who experienced disease progression within 3 months of first-line platinum therapy.
• Participants with a known BRCA 1 or 2 mutation.
• Participant has received prior therapy with an anti-PD-1, anti-PD-L1 or anti-PD-L2 agent.
• Participant has received prior therapy with a PARP-1/PARP-2 inhibitor.
• Participant has a known hypersensitivity to dostarlimab (TSR-042), Niraparib, their components, or their excipients.
• Participant has a known history of myelodysplastic syndrome or acute myeloid leukemia.
• Participant has not recovered from prior chemotherapy induced adverse events (AEs).
• Participant has a known diagnosis of immunodeficiency or is receiving systemic steroid therapy exceeding an equivalent of prednisone 10 mg daily or any other form of immunosuppressive therapy within 7 days prior to the first dose of study treatment.
• Participant is currently participating in a treatment study or has participated in a study of an investigational agent within 4 weeks of the first dose of treatment.
• Participant has received prior systemic anticancer therapy including cytotoxic chemotherapy, hormonal therapy given with the intention to treat ovarian cancer, or biological therapy within 3 weeks of the first dose of study treatment.
• Participant has received live vaccine within 14 days of planned start of study therapy
• Participant has symptomatic uncontrolled brain or leptomeningeal metastases. (If investigator feels participant symptoms are not symptomatic, participants can undergo a scan to confirm for eligibility).
• Participant had major surgery with 4 weeks of starting the study or participant has not recovered from any effects of any major surgery.
• Participant has a known additional malignancy that progressed or required active treatment within the last 2 years.
• Participant is considered a poor medical risk due to a serious, uncontrolled medical disorder, nonmalignant systemic disease or active controlled infection.
• Participant has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study.
• Participant has known active hepatitis B (hepatitis B surface antigen reactive) or hepatitis C (hepatitis C virus ribonucleic acid, qualitative).

• Participant with a known history of human immunodeficiency virus (HIV) are allowed if they meet all of the following criteria:

  1. Cluster of differentiation 4 >=350/μL and viral load <400 copies/milliliter (mL)
  2. No history of acquired immunodeficiency syndrome-defining opportunistic infections within 12 months prior to enrollment
  3. No history of HIV-associated malignancy for the past 5 years
  4. Concurrent antiretroviral therapy as per the most current National Institutes of Health (NIH) Guidelines for the Use of Antiretroviral Agents in Adults and Adolescents Living with HIV started >4 weeks prior to study enrollment
• Participant is immunocompromised. Participants with splenectomy are allowed.
• Participant has an ongoing bowel obstruction or has other conditions that would lead to impaired absorption of oral niraparib.
• Participant has active autoimmune disease that has required systemic treatment in the past 2 years (ie, with use of disease-modifying agents, corticosteroids, or immunosuppressive drugs). Replacement therapy (eg, thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment.