Study of Nivolumab and Axitinib in Patients With Advanced Renal Cell Carcinoma

Inclusion Criteria: * Histologically or cytologically confirmed advanced RCC with predominantly clear cell subtype. * Archival tumor biospecimen (when available) must be procured for correlative evaluation. If tumor tissue is not available or accessible despite good faith efforts, patient may still be treated on study. * Formalin fixed, paraffin embedded \[FFPE\] tissue block(s) or at least 12 unbaked, unstained slides are required. Tissue samples taken from a metastatic lesion prior to the start of screening are acceptable. * At least one measurable lesion as defined by RECIST version 1.1. * Age \> 18 years. * ECOG performance status 0 or 1 * Adequate bone marrow, kidney, and liver function as defined by: WBC ≥ 2000/μL. Neutrophils ≥ 1500/μL. Platelets ≥ 100 x103/μL. Hemoglobin \> 9.0 g/dL. Serum creatinine ≤ 1.5 x ULN or creatinine clearance (CrCl) ≥ 40 mL/min (if using the Cockcroft-Gault formula): Female CrCl = (140 - age in years) x (weight in kg x 0.85)/(72 x serum creatinine in mg/dL). Male CrCl = (140 - age in years) x (weight in kg x 1.00)/(72 x serum creatinine in mg/dL). AST/ALT ≤ 3 x ULN. Total Bilirubin ≤ 1.5 x ULN (except subjects with Gilbert Syndrome, who can have total bilirubin \< 3.0 mg/dL). * No evidence of pre-existing uncontrolled hypertension as documented by 2 baseline blood pressure (BP) readings taken at least 1 hour apart. The baseline systolic BP readings must be ≤ 150 mm Hg, and the baseline diastolic BP readings must be ≤ 90 mm Hg * Patients enrolled to the prior treatment arm of the expansion cohort must have been exposed to a TKI for metastatic disease OR treated with the combination of ipilimumab and nivolumab in the 1st line setting for metastatic disease. Exposure to TKI as part of (neo)adjuvant treatment that completed within 1 year of study qualifies as prior exposure as well. Prior high dose interleukin-2 is allowed and patients who received this as their only prior line of treatment for metastatic disease may be included in the treatment naïve group. Exclusion Criteria: * Prior therapy with axitinib * Prior systemic therapy directed at advanced RCC is not allowed for patients enrolled to the expansion cohort, treatment naïve arm. If prior (neo)adjuvant treatment given as part of a clinical trial, this would be allowed as long as last dose was \> 1 year prior to start of treatment * Patients enrolled to the prior treatment arm of the dose escalation cohort must not have received anti-cancer therapy less than 14 days prior to the first dose of study drug or palliative, focal radiation therapy less than 14 days prior to the first dose of study drug. * Patients are excluded if they have active, symptomatic brain metastases or leptomeningeal metastases. Subjects with known brain metastases are eligible if metastases have been treated and there is no magnetic resonance imaging (MRI) evidence of progression for four weeks (after treatment is complete and within 28 days prior to study drug administration. * Second malignancy requiring active systemic treatment * Diagnosis of immunodeficiency * Active, known or suspected autoimmune disease. Subjects are permitted to enroll if they have vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger * Patients have a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration. Inhaled or topical steroids and adrenal replacement doses \> 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease. * Major surgery \<4 weeks or radiation therapy \<2 weeks of study entry. Prior palliative radiotherapy to metastatic lesion(s) is permitted, provided there is at least one measurable lesion that has not been irradiated. * Gastrointestinal abnormalities including: Inability to take oral medication; Requirement for intravenous alimentation; Prior surgical procedures affecting absorption including total gastric resection; Treatment for active peptic ulcer disease in the past 6 months; Active gastrointestinal bleeding as evidenced by hematemesis, hematochezia or melena in the past 3 months without evidence of resolution documented by endoscopy or colonoscopy; Malabsorption syndromes. * Evidence of inadequate wound healing. * Active bleeding disorder or other history of significant bleeding episodes within 30 days before study entry. * Known prior or suspected hypersensitivity to study drugs or any component in their formulations. * Current use or anticipated need for treatment with drugs or foods that are known strong CYP3A4/5 inhibitors including but not limited to atazanavir, clarithromycin, indinavir, itraconazole, ketoconazole, nefazodone, nelfinavir, ritonavir, saquinavir, telithromycin, troleandomycin, voriconazole, and grapefruit or grapefruit juice. The topical use of these medications (if applicable), such as 2% ketoconazole cream, is allowed. * Current use or anticipated need for treatment with drugs that are known strong CYP3A4/5 inducers, including but not limited to carbamazepine, phenobarbital, phenytoin, rifabutin, rifampin, and St. John's wort. * As there is potential for hepatic toxicity with nivolumab, drugs with a predisposition to hepatotoxicity should be used with caution in patients treated with nivolumab-containing regimen. * Known hepatitis B virus (HBV) or hepatitis C virus (HBV) infection. * Known history of human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) * History of any of the following cardiovascular conditions within 12 months of screening: Myocardial infarction, Unstable angina pectoris, Cardiac angioplasty or stenting, Coronary/peripheral artery bypass graft, Class III or IV congestive heart failure per New York Heart Association, Cerebrovascular accident or transient ischemic attack * History of deep vein thrombosis or pulmonary embolism within 6 months of screening. Patients who are currently taking anticoagulation therapy for a prior history (\> 6 months from screening) of thrombosis may still be eligible. * Pregnant or breast feeding.