HERV-E TCR Transduced Autologous T Cells in People With Metastatic Clear Cell Renal Cell Carcinoma

* INCLUSION CRITERIA: * Patients must have histologically confirmed RCC with clear-cell component by the Laboratory of Pathology of the NIH and/or outside Pathology Department prior to entering this study. * Patients must be HLA-A 11:01 positive (confirmed by HLA typing at the NIH DTM) * Patients must have measurable disease per RECIST version 1.1 and have disease progression during or after the last treatment regimen and within 6 months before study enrollment * Patients must have received at least one antiangiogenic drug and an immune-checkpoint inhibitor (i.e. nivolumab) unless the patient has contraindications to receiving these medications, the agents are not available to the patient, or the patient declines to receive these drugs due to personal preference. * Patients must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, the duration of study participation and 180 days (female patients) or 90 days (male patients) after the end of the treatment if sexually active and able to bear or beget children. In addition, male patients must refrain from sperm donation for 90 days after the final dose of investigational product. Female patients must refrain from egg cell donation for 180 days after the final dose of investigational product * Patients must be between the ages of 18 and 75 years. * Patient must have an anticipated life expectancy of at least 3 months. * Patients must have a performance status of 0 or 1 ECOG performance status (PS) scale. * Patients must have a caregiver willing to stay with them during the first month of treatment (30 days +/- 7 days). * Patients receiving treatment with bisphosphonates or denosumab are eligible for enrollment if on a stable dose for greater than or equal to 4 weeks * Serology: * Seronegative for HIV antibody. (The experimental treatment being evaluated in this protocol depends on an intact immune system. Patients who are HIV seropositive can have decreased immune-competence and thus be less responsive to the experimental treatment and more susceptible to its toxicities.) * Seronegative for hepatitis B antigen, and seronegative for hepatitis C antibody. If hepatitis C antibody test is positive, then patient must be tested for the presence of antigen by RT-PCR and be HCV RNA negative. * Organ Function * Hematology * Absolute neutrophil count greater than or equal to 500/ microL * WBC greater than or equal to 1500/microL * Platelet count greater than or equal to 75.000/microL (without transfusional support * Chemistry * Serum AST/ALT less than or equal to 2.5 x upper limit of normal (ULN) * Total bilirubin less than or equal to 1.5 mg/dl except for patients with Gilbert s syndrome who must have a total bilirubin less than or equal to 3 mg/dl * Creatinine clearance greater than or equal to 50 ml/min/1.73m\^2 by the method of CKI-EPI or \>=50 ml/min by the method of 24h Clearence of Creatinine Calculation * INR \< 1.5 * Cardiology * Estimated left ventricular ejection fraction by echocardiography greater than or equal to 45% * Respiratory * Predicted DLCO / Alveolar Volume Adjusted by PFT \>= 45% EXCLUSION CRITERIA: * Patients that require immediate therapy due to tumor mass effects or spinal cord compression. * Patients must not have had standard of care anti-VEGFR therapy (mean half-life around 30 hours), mTOR inhibitors (mean half-life around 30 hours), at least for the last 7 days prior to T-cell infusion and radiotherapy, or major surgery within the last 2 weeks prior to T-cell infusion. For PD-1/PD-L1 inhibitors or CTLA-4 inhibitors, a 4-week period must have elapsed before T-cell infusion. For recent experimental therapies a 28-day period must have elapsed before infusing expanded T-cells. * Patients with active CNS involvement by malignancy either by imaging or cerebrospinal fluid involvement or biopsy-proven (due to poor prognosis and potential for neurological dysfunction that would confound evaluation of neurological and other adverse events) except for: 1. Patients with 3 or fewer brain metasteses of \<1cm treated with either stereotactic or gamma knife radiotherapy and remained stable on MRI for 2 weeks are eligible. 2. Patients with surgically resected brain metastases and no evidence of active disease in the CNS at the time of screening evaluation are eligible. * Patients with hypercalcemia (\>10 mg/dL) of malignancy. * Any prior Grade greater than or equal to 3 immune-related adverse event (irAE) while receiving immunotherapy, including anti-CTLA4 treatment that requires long-term immunosuppressive therapy. Note: Active or history of vitiligo or hypothyroidism will not be a basis for exclusion. * Patients with second malignancies in addition to their clear cell RCC are not eligible if the second malignancy has required systemic treatment within the past 4 years or is not in complete remission. There are exceptions to this criterion: successfully treated non-metastatic basal cell, squamous cell skin carcinoma, in situ non-invasive cervical cancer and in situ non-invasive breast cancer. * Women of child-bearing potential who are pregnant or breastfeeding because of the potentially dangerous effects of the preparative chemotherapy on the fetus or infant. * Active coagulation disorders or other major uncontrolled medical illnesses of the respiratory, endocrine, renal, gastrointestinal, genitourinary or immune system, uncontrolled systemic infection, active obstructive or restrictive pulmonary disease. * Patients who have recent history of cerebrovascular accident, transient ischemic attack should be cleared by the neurology consult service before enrolling this study. * Patients who have recent history of coronary artery disease or cardiac arrhythmia should be cleared by the cardiology consult service before enrolling this study. * Any form of primary immunodeficiency (such as Severe Combined Immunodeficiency Disease). * Patients with autoimmune diseases such as Crohn's disease, ulcerative colitis, rheumatoid arthritis, autoimmune hepatitis or pancreatitis, and systemic lupus erythematosus that requires treatment with chronic immunosuppressive therapy. * Systemic corticosteroid steroid therapy of any dose is not allowed within 2 days prior to enrollment. * The following are exceptions to this criterion: * Intranasal, inhaled, and topical steroids * Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or equivalent * Steroids as premedication for hypersensitivity reactions (e.g., CT scan premedication). * History of severe immediate hypersensitivity reaction to any of the agents used in this study. * Unable to understand the investigational nature of the study or give informed consent and does not have a legally authorized representative or surrogate that can provide informed consent. * Any condition that, in the opinion of the investigator, would interfere with evaluation of the investigational product or interpretation of subject safety or study results.