Olaparib and Entinostat in Patients With Recurrent, Platinum-Refractory, Resistant Ovarian, Primary Peritoneal, Fallopian Tube Cancers

Inclusion Criteria: * High-grade carciomas of the ovary, fallopian tube, or periteonum, based on local pathology review, including high grade serous carcinoma, high grade endometrioid carcinomas, clear cell carcinoma, and carcinosarcoma. * Platinum-refractory or resistant disease, as defined by progressive disease while receiving platinum-based chemotherapy or with recurrent disease \< 6 months after the completion of platinum-based chemotherapy. * May have received up to 2 prior therapies for platinum-resistant ovarian cancer. * Must have received prior-platinum-based chemotherapy. * BRCA1, BRCA2, RAD51, BRIP1, ATM, FANCL, PALB2 and other FA/BRCA pathway gene wild-type. * Tumor HR-proficient, as assessed by Myriad myChoice HRD Test (HRD score \< 42). * Provision of informed consent prior to any study specific procedures * Patients must have normal organ and bone marrow function measured within 28 days prior to administration of study treatment as defined below: * Haemoglobin ≥ 10.0 g/dL with no blood transfusion in the past 28 days * 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 (AST) (Serum Glutamic Oxaloacetic Transaminase (SGOT)) / Alanine aminotransferase (ALT) (Serum Glutamic Pyruvate Transaminase (SGPT)) ≤ 2.5 x institutional upper limit of normal unless liver metastases are present in which case they must be ≤ 5x ULN * Patients must have creatinine clearance estimated using the Cockcroft-Gault equation of ≥51 mL/min: Estimated creatinine clearance = (140-age \[years\]) x weight (kg) (x 0.85) serum creatinine (mg/dL) x 72 * Ideal body weight will be used, unless actual weight is less than ideal * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Patients must have a life expectancy ≥ 16 weeks. * Postmenopausal or evidence of non-childbearing status for women of childbearing potential: negative urine or serum pregnancy test within 28 days of study treatment and confirmed prior to treatment on day 1. Postmenopausal is defined as: * Amenorrheic for 1 year or more following cessation of exogenous hormonal treatments * Luteinizing hormone (LH) and Follicle stimulating hormone (FSH) levels in the post menopausal range for women under 50 * Radiation-induced oophorectomy with last menses \>1 year ago * Chemotherapy-induced menopause with \>1 year interval since last menses * Surgical sterilisation (bilateral oophorectomy or hysterectomy) * Patient is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations. * At least one lesion, not previously irradiated, that can be accurately measured at baseline as ≥ 10 mm in the longest diameter (except lymph nodes which must have short axis ≥ 15 mm) with computed tomography (CT) or magnetic resonance imaging (MRI) and which is suitable for accurate repeated measurements. * Formalin fixed, paraffin embedded (FFPE) tumor sample or slides from the primary cancer must be available for myRisk HRD testing. If there is not written confirmation of the availability of an archived tumor sample prior to enrolment the patient is not eligible for the study. Additionally, a second FFPE tumor sample OR 10 unstained slides must be available for performance of correlative studies. The patient must provide separate informed consent to obtain the optional tumor biopsy. If a patient declines to participate in the optional tissue biopsy, there will be no penalty or loss of benefit to the patient. The patient will not be excluded from other aspects of the study. Exclusion Criteria: * Involvement in the planning and/or conduct of the study (applies to both AstraZeneca staff and/or staff at the study site) * Previous enrollment in the present study * Participation in another clinical study with an investigational product during the last 4 weeks. * Any previous treatment with PARP inhibitor, including olaparib. * Any previous treatment with an HDAC inhibitor, including entinostat. * Low grade or borderline epithelial ovarian, fallopian tube, or peritoneal cancers, sex- cord stromal tumors of the ovary, germ cell tumors of the ovary. * Patients with known germline mutations of BRCA1, BRCA1, RAD51, ATM, FANCL, PALB2, and other FA/BRCA pathway genes. * Patients whose tumors are HR-deficient, as measured by Myriad myChoice HRD test * Other malignancy within the last 5 years except: 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, or other solid tumours including lymphomas (without bone marrow involvement) curatively treated with no evidence of disease for ≥5 years. Patients 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 patient remains free of recurrent or metastatic disease * Resting ECG with QTcF \> 470 msec on 2 or more time points within a 24 hour period or family history of long QT syndrome * If the first ECG shows QTcF \> 470 msec, a second ECG within 24 hours would need to be completed * Patients receiving any systemic chemotherapy or radiotherapy (except for palliative reasons) within 3 weeks prior to study treatment. * Concomitant use of known strong CYP3A inhibitors (eg. itraconazole,telithromycin, clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir) or moderate CYP3A inhibitors (eg. ciprofloxacin, erythromycin, diltiazem, fluconazole,verapamil). See https://secure.medicalletter.org/system/files/private/TML-article1491e.pdf for a more complete list. The required washout period prior to starting olaparib is 2 weeks. * Concomitant use of known strong (eg. phenobarbital, enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine and St John's Wort ) or moderate CYP3A inducers (eg. bosentan, efavirenz, modafinil). See https://secure.medicalletter.org/system/files/private/TML-article-1491e.pdf for a more complete list. The required washout period prior to starting olaparib is 5 weeks for enzalutamide or phenobarbital and 3 weeks for other agents. * Persistent toxicities (\>Common Terminology Criteria for Adverse Event (CTCAE) grade 2) caused by previous cancer therapy, excluding alopecia. * Patients with myelodysplastic syndrome/acute myeloid leukaemia or with features suggestive of MDS/AML * Patients with symptomatic uncontrolled brain metastases. A scan to confirm the absence of brain metastases is not required. The patient can receive a stable dose of corticosteroids before and during the study as long as these were started at least 4 weeks prior to treatment. Patients with spinal cord compression unless considered to have received definitive treatment for this and evidence of clinically stable disease for 28 days. * Major surgery within 2 weeks of starting study treatment and patients must have recovered from any effects of any major surgery. * Patients 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 hypertension, recent bleeding diathesis, 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. * Patients unable to swallow orally administered medication and patients with gastrointestinal disorders likely to interfere with absorption of the study medication. * Breast feeding women. * Patients, e.g., patients who are known to be serologically positive for human immunodeficiency virus (HIV). * Patients with a known hypersensitivity to olaparib or any of the excipients of the product. * Patients with a known hypersensitivity to entinostat or any of the excipients of the product. * Patients with known active hepatitis (i.e. Hepatitis B or C) due to risk of transmitting the infection through blood or other body fluids * Previous allogenic bone marrow transplant or double umbilical cord blood transplantation (dUCBT) * Whole blood transfusions in the last 120 days prior to entry to the study. * Patients taking warfarin