Inclusion Criteria:  Females age ≥ 18 years (at time of signing informed consent) ECOG status 0 or 1 Pathologically documented ovarian, fallopian tube, or primary peritoneal carcinoma. Progression on prior PARPi (progressed while on PARPi or within 6 months of completing PARPi therapy) either as maintenance or therapeutic settings. Platinum-sensitive disease: progressed after > 6 months of completing prior platinum therapy. Have had no more than 5 prior cancer therapy treatment regimens, of which a maximum of 4 were cytotoxic chemotherapy or DNA-damage response agents (likel PARPi) containing regimens Measurable disease per RECIST 1.1 Known BRCA1/2 status  Adequate laboratory parameters at Screening including:  Hemoglobin ≥ 9.0 gm/dL without transfusions during the 4 weeks prior to Screening Absolute neutrophil count (ANC) ≥ 1.5 × 109/L Platelet count ≥ 150,000/mm3 Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) ≤ 2.0 x ULN or if liver function abnormalities due to liver metastases AST and ALT ≤ 5.0 x ULN Total bilirubin ≤ 1.5 x ULN (≤ 3.0 x ULN for subjects with known Gilbert's syndrome) Calculated (Cockcroft-Gault formula) or measured creatinine clearance ≥ 60 mL/min Prothrombin time (PT), international normalized ratio (INR) and partial thromboplastin time (PTT) < 1.5 x ULN Female subjects may be enrolled if they are not of childbearing potential, permanently sterile or who are post-menopausal, defined as no menses for at least 1 year without an alternative medical cause and FSH levels in the post-menopausal range. Female subjects of childbearing potential may be enrolled if they consistently and correctly use a highly effective form of contraception. Highly effective forms of contraception include: combined (estrogen and progestogen hormonal contraceptives (oral, intravaginal, transdermal) associated with inhibition of ovulation; progestogen-only hormonal contraception (oral, injectable, implantable) associated with inhibition of ovulation; intrauterine device (IUD); intrauterine hormone-releasing system (IUS); bilateral tubal occlusion; vasectomized partner; sexual abstinence. Female subjects should not donate eggs from the time point of study drug administration until at least 7 months thereafter Females of childbearing potential must have a negative serum pregnancy test before the first dose of study drug and must agree to serum pregnancy tests during the study. Females may not be breast-feeding at the first dose of study drug, during study participation or through 7 months after the last dose of study drug. Ability to swallow capsules and comply with study procedures. Ability to understand and willingness to sign informed consent form prior to initiation of any study procedures. Patients with previously diagnosed brain metastases are eligible if they have completed their treatment and have recovered from the acute effects of radiation therapy or surgery prior to study enrollment, have discontinued corticosteroid treatment for these metastases for at least 4 weeks and are neurologically stable with evidence of no disease progression for 6 months.  Exclusion Criteria:  Patients with platinum-resistant or primary platinum refractory cancer (progressing during primary platinum therapy or within 3 months of completing primary first line platinum therapy) Current or anticipated use of medications known to be strong inhibitors or inducers of CYP3A4 or substrates of CYP1A2 with narrow therapeutic windows. Strong inhibitors, inducers or substrates must be discontinued at least 7 days prior to the first administration of study drug. Current or anticipated use within 7 days prior to the first administration of study drug, or during the study, of strong P-gp inhibitors. For a list of strong P-gp inhibitors. Use of oral Factor Xa inhibitors (i.e., rivaroxaban, apixaban, betrixaban, edoxaban otamixaban, letaxaban, eribaxaban) and Factor IIa inhibitors (i.e., dabigatran). Low molecular weight heparin is allowed Radiation to >25% of the bone marrow Treatment with a bone-targeted radionuclide within 6 weeks of first dose of study drug Prior chemotherapy or radiation within 3 weeks of study enrollment Have previously received an investigational BET inhibitor (including previous participation in studies with Zenith drug, ZEN003694) QTcF interval > 470 msec Insufficient recovery from prior treatment-related toxicities except for alopecia, fatigue and uncontrolled Grade 2 neuropathy Non-healing wound, ulcer or bone fracture (not including a pathological bone fracture caused by a pre-existing pathological bone lesion) Brain metastases not adequately treated and/or clinically stable (at the discretion of the Investigator) for at least 6 months prior to the start of study treatment Patients with ovarian carcinosarcoma Known impaired cardiac function or clinically significant cardiac disease such as uncontrolled supraventricular arrhythmia, ventricular arrhythmia requiring therapy, or congestive heart failure (New York Heart Association functional class III or IV) Myocardial infarction or unstable angina within 6 months prior to the first administration of study drug Known myelodysplastic syndrome Other clinically significant co-morbidities, such as uncontrolled pulmonary disease, active central nervous system disease, active, uncontrolled bacterial, viral, or fungal infection(s) requiring systemic therapy, or any other condition that could compromise safety or the patient's participation in the study Impairment of gastrointestinal function that may significantly alter the absorption of ZEN003694 or talazoparib Other known active cancer requiring therapy at time of study entry or that progressed or required treatment within 3 years prior to starting study drug (except for skin basal cell carcinoma or squamous cell carcinoma or in situ cervical cancer)  History of infection with (screening tests not required): human immunodeficiency virus; hepatitis B virus with currently active disease defined as hepatitis B surface antigen (HBsAg) positivity; or hepatitis C virus unless previously treated and viral load is undetectable except following situations:  HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months of enrollment are eligible for this trial. Patients with 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 are allowed to be included if: participant on a stable dose of antiviral therapy, HBV viral load below the limit of quantification. HCV viral load below the limit of quantification. Major surgery other than diagnostic surgery, dental surgery or stenting within 4 weeks prior to the first administration of study drug Concurrent participation in another clinical investigational treatment trial. Any other reason that in the opinion of the Investigator would prevent the patient from completing participation or following the study.