This phase III trial compares the effect of adding tivozanib to standard therapy pembrolizumab versus pembrolizumab alone for the treatment of patients with high-risk renal cell carcinoma (RCC). Immunotherapy with monoclonal antibodies, such as pembrolizumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Tivozanib is in a class of medications called kinase inhibitors. It works by blocking the action of the abnormal protein that signals tumor cells to multiply. This helps stop the spread of tumor cells. Giving pembrolizumab and tivozanib together may work better than pembrolizumab alone in treating patients with RCC.