Avelumab (Bavencio) With IL-15 in Subjects With Clear-Cell Renal Carcinoma

Background: -Clear-cell renal cell carcinoma (ccRCC) is a kind of kidney cancer. The drug avelumab may help direct the immune response to the tumors and can prolong the immune response. The drug Interleukin-15 (IL-15) stimulates certain kinds of white blood cells that have the potential to attack the cancer. Objective: -To test whether IL-15 and avelumab administered together are safe and effective at treating ccRCC. Eligibility: -People ages 18 and older with relapsed, metastatic biopsy proven clear cell renal cell carcinoma (ccRCC) that has not responded to standard treatments Design: Participants will be screened with: * Medical history * Physical exam * Blood, urine, heart, and lung tests * Computed tomography (CT) and positron emission tomography (PET) scans and possible MRI: Participants will lie in a machine that takes pictures of the body. For the CT scan, they may receive an oral contrast agent by mouth and normally receive IV contrast through a vein to improve the x-ray images. * Tumor sample to confirm expression of avelumab target: If one is not available, participants will require a new biopsy that is generally obtained by a needle that is inserted into the tumor. Participants will get the study drugs by vein for up to four 28-day cycles. The IL-15 will be given through a vein continuously for the first 5 days (120 hours) of each cycle. They avelumab will be given through a vein over about 1 hour on days 8 and 22 of each cycle. Participants will be hospitalized for their 1st week of IL-15 cycle and may be able to receive their subsequent IL-15 treatment as an outpatient depending on their side effects. Participants who receive the infusion as an outpatient will return to the hospital each day for a new bag of IL-15. Participants who cannot or do not want to be treated as an outpatient will be treated in the hospital during their 5-day IL-15 infusions. * Participants will need a midline venous catheter which is longer than a standard venous catheter but is still inserted into a peripheral vein in their arm. * Participants will have repeats of blood tests to monitor the blood counts and chemistry throughout the study. * Participants will have follow-up visits 30 days after their last treatment, every 60 days for the first 6 months, every 90 days for 2 years, then every 6 months.