This phase III trial compares the effect of pembrolizumab to active surveillance after a surgical procedure to completely or partially remove a kidney (nephrectomy) in improving time without disease in patients with non-clear cell renal cell cancer. 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. Giving pembrolizumab after nephrectomy may be more effective than the usual active surveillance approach for improving time without disease in patients with non-clear cell renal cell cancer.