Study of Entinostat With Nivolumab Plus Ipilimumab in Previously Treated Renal Cell Carcinoma

Inclusion Criteria: * Written informed consent and HIPAA authorization for release of personal health information. NOTE: HIPAA authorization may be included in the informed consent or obtained separately. * Age ≥ 18 years at the time of consent. * Eastern Cooperative Oncology Group (ECOG) Performance Status of 0-1 within 28 days prior to registration. * Histological or cytological evidence of renal cell carcinoma (initial diagnosis). * Metastatic disease * Progressive disease (PD) on nivolumab + ipilimumab regimen. Note: Patients who have completed at least one dose of ipilimumab + nivolumab and progress or have completed the 4 doses of ipilimumab + nivolumab and progress during nivolumab monotherapy maintenance are eligible unless they have received additional treatment(s) for their renal cell carcinoma prior to registration. Patients who discontinue prior ipilimumab + nivolumab or nivolumab monotherapy for toxicity are excluded. Patients who receive nivolumab or other anti-PD-1/PD-L1 agents as subsequent therapy after ipilimumab + nivolumab are excluded. * Target lesions according to RECIST v1.1 or non-target bone lesions assessed by bone scan or positron emission tomography (PET) scan. * A subject with prior brain metastasis may be considered if they have completed their treatment for brain metastasis at least 4 weeks prior to study registration, have been off corticosteroids for ≥ 4 weeks, and are asymptomatic. * Prior cancer treatment (excluding nivo/ipi) must be completed at least 28 days prior to registration and the subject must have recovered from all reversible acute toxic effects of the regimen (other than alopecia or neuropathy) to ≤Grade 1 or baseline. If subject underwent major surgery or radiation therapy of \>30 Gy, they must have recovered from the toxicity and/or complications from the intervention. * Demonstrate adequate organ function as defined in the table below; all screening labs to be obtained within 28 days prior to registration * Platelets ≥100 x 10\^9/L * Absolute Neutrophil Count (ANC) ≥1.5 x 10\^9/L * Hemoglobin (Hgb) ≥9 g/dL or ≥5.6 mmol/L * Creatinine OR Measured or calculated creatinine clearance (CrCl) (glomerular filtration rate \[GFR\] can also be used in place of CrCl) Creatinine clearance should be calculated per institutional standard ≤1.5 x the upper limit of normal (ULN) OR ≥60 mL/min for subject with creatinine levels \>1.5 x institutional ULN * Bilirubin ≤1.5 x ULN OR Direct bilirubin ≤ ULN for subjects with total bilirubin levels \> 1.5 x ULN * Aspartate aminotransferase (AST) ≤3 x ULN * Alanine aminotransferase (ALT) ≤3 x ULN * International Normalized Ratio (INR) or Prothrombin Time (PT) Activated Partial Thromboplastin Time (aPTT) ≤ 1.5 × ULN unless subject is receiving anticoagulant therapy as long as PT/INR/PTT is within therapeutic range of intended use of anticoagulants * Women of childbearing potential (WOCBP) must have a negative serum pregnancy test during screening and a negative urine pregnancy test within 3 days prior to first dose of study drug. If the screening serum test is done within 3 days prior to receiving the first dose of study drug, a urine test is not required. * Women of childbearing potential must be willing to abstain from heterosexual intercourse or to use an effective method of contraception from the time of informed consent until 5 months after the last dose of study drug. * Men who are sexually active with WOCBP must use any contraceptive method with a failure rate of less than 1% per year. Men receiving study drugs and who are sexually active with WOCBP will be instructed to adhere to contraception for a period of 3 months after the last dose of entinostat. * As determined by the enrolling physician or protocol designee, ability of the subject to understand and comply with study procedures for the entire length of the study. * Life expectancy of at least 6 months per investigator discretion. Exclusion Criteria: * Subjects meeting any of the criteria below may not participate in the study: * History or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the subject to participate, in the opinion of the treating investigator, including, but not limited to: * Myocardial infarction or arterial thromboembolic events within 6 months prior to screening or severe or unstable angina, New York Heart Association (NYHA) Class III or IV disease, or a corrected QT interval (QTc) interval \> 470 msec. * Uncontrolled hypertension or diabetes mellitus. * Another known malignancy that is progressing or requires active treatment. * Any prior history of other cancer within the prior 5 years with the exception of adequately treated basal cell carcinoma or cervical intraepithelial neoplasia \[CIN\]/cervical carcinoma in situ or melanoma in situ). * Active infection requiring systemic therapy. * Known active central nervous system (CNS) metastases and/or carcinomatous meningitis. * Pregnant or breastfeeding. Note: breast milk cannot be stored for future use while the mother is being treated on study. * Any contraindication to oral agents or significant nausea and vomiting, malabsorption, or significant small bowel resection that, in the opinion of the investigator, would preclude adequate absorption. * Allergy to benzamide or inactive components of entinostat. * Hypersensitivity to nivolumab, ipilimumab, or any of their excipients. * Treatment with any investigational drug or device within 4 weeks prior to registration. * Treatment with systemic steroids within 4 weeks prior to registration. Note: adrenal replacement doses of steroids (for example prednisone 10mg daily) are permitted while on study. * Evidence of active autoimmune disease requiring systemic treatment within the past 90 days or a documented history of clinically severe autoimmune disease, or a syndrome that requires systemic steroids or immunosuppressive agents. Subjects with vitiligo or resolved childhood asthma/atopy would be an exception to this rule. Subjects that require intermittent use of bronchodilators or local steroid injections would not be excluded from the study. Subjects with hypothyroidism stable on hormone replacement or Sjogren's syndrome will not be excluded from the study. * Interstitial lung disease or history of pneumonitis requiring treatment with corticosteroids. * Diagnosis of immunodeficiency; or is receiving chronic systemic corticosteroid therapy or other immunosuppressive therapy (excludes inhaled corticosteroids) within 4 weeks prior to registration. * Known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies). Testing during screening is not required. * Known active hepatitis B (e.g., hepatitis B surface antigen-reactive) or hepatitis C (e.g., hepatitis C virus ribonucleic acid \[qualitative\]). Subjects with past hepatitis B virus (HBV) infection or resolved HBV infection (defined as the presence of hepatitis B core antibody \[HBc Ab\] and absence of HBsAg) are eligible. HBV DNA test must be performed in these subjects prior to study treatment, and results must be negative to be eligible. Subjects with a history of hepatitis C must be tested for presence of hepatitis C virus (HCV) antibody. If HCV antibody positive, subjects will only be eligible if polymerase chain reaction is negative for HCV RNA. * Has received a live vaccine within 30 days prior to planned start of study therapy. Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however, intranasal influenza vaccines (e.g., Flu-Mist®) are live attenuated vaccines, and are not allowed.