Nivolumab in Treating Patients With High-Risk Kidney Cancer Before Surgery

Inclusion Criteria: * Patients must have histologically or cytologically confirmed clear cell renal cell carcinoma (RCC) * For non-metastatic patients, the preoperative Memorial Sloan-Kettering (MSK) nomogram estimates the patient's likelihood of freedom from metastatic recurrence within the first 12 years following radical or partial nephrectomy to be =\< 80% * Measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm (\>= 2 cm) with conventional techniques or as \>= 10 mm (\>= 1 cm) with spiral computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam * Non-metastatic disease will be defined by no evidence of metastases other than regional lymphadenopathy as assessed by imaging of the chest, abdomen and pelvis with CT of the chest and CT or MRI of the abdomen; regional lymph nodes, per 7th edition American Joint Committee on Cancer (AJCC) staging manual (2010) for kidney cancer, include the following positions: renal hilar, precaval, paracaval, retrocaval, interaortocaval, paraaortic, preaortic, and retroaortic * Scheduled to undergo nephrectomy or metastasectomy as part of treatment plan, per assessment through an MSK urologic surgeon or medical oncologist listed as investigator on this trial * Availability of a frozen biopsy core prior to cycle 1, day 1 * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 (Karnofsky \>= 80%) * Leukocytes \>= 2,500/mcL * Absolute neutrophil count \>= 1,500/mcL (without granulocyte colony-stimulating factor support within 2 weeks prior to cycle 1, day 1) * Platelets \>= 100,000/mcL (without transfusion within 2 weeks prior to cycle 1, day 1) * Hemoglobin \>= 9.0 g/dL (patients may be transfused to meet this criterion) * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (except patients with Gilbert syndrome, who can have total bilirubin \< 3.0 mg/dL) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x ULN * Creatinine =\< 1.5 x ULN OR creatinine clearance (CrCl) \>= 50 mL/min (if using the Cockcroft-Gault formula) * The effects of nivolumab on the developing human fetus are unknown; for this reason, women of child-bearing potential (WOCBP) and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; WOCBP should use an adequate method to avoid pregnancy for 23 weeks after the last dose of investigational drug; women of childbearing potential must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin \[HCG\]) within 14 days prior to the start of nivolumab; women must not be breastfeeding; men who are sexually active with WOCBP must use any contraceptive method with a failure rate of less than 1% per year; men receiving nivolumab and who are sexually active with WOCBP will be instructed to adhere to contraception for a period of 31 weeks after the last dose of investigational product; women who are not of childbearing potential (i.e., who are postmenopausal or surgically sterile as well as azoospermic men) do not require contraception * Women of childbearing potential (WOCBP) is defined as any female who has experienced menarche and who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy) or who is not postmenopausal; menopause is defined clinically as 12 months of amenorrhea in a woman over 45 in the absence of other biological or physiological causes; in addition, women under the age of 55 must have a documented serum follicle stimulating hormone (FSH) level greater than 40 mIU/mL * WOCBP receiving nivolumab will be instructed to adhere to contraception for a period of 23 weeks after the last dose of investigational product; men receiving nivolumab and who are sexually active with WOCBP will be instructed to adhere to contraception for a period of 31 weeks after the last dose of investigational product; these durations have been calculated using the upper limit of the half-life for nivolumab (25 days) and are based on the protocol requirement that WOCBP use contraception for 5 half-lives plus 30 days and men who are sexually active with WOCBP use contraception for 5 half-lives plus 90 days * Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she (or the participating partner) should inform the treating physician immediately * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Prior receipt of systemic checkpoint inhibitor therapy for renal cell carcinoma * Inability to safely delay surgery by 8 weeks as per surgeon's discretion * Patients who are receiving any other investigational agents * History of allergic reactions attributed to compounds of similar chemical or biologic composition to nivolumab * History of severe hypersensitivity reaction to any monoclonal antibody * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because nivolumab has a potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with nivolumab, breastfeeding should be discontinued if the mother is treated with nivolumab * Patients should be excluded if they have known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) * Patients should be excluded if they have a positive test for hepatitis B virus surface antigen (HBV sAg) or hepatitis C virus ribonucleic acid (HCV RNA) indicating acute or chronic infection * Patients with active autoimmune disease or history of autoimmune disease that might recur, which may affect vital organ function or require immune suppressive treatment including systemic corticosteroids, should be excluded; these include but are not limited to patients with a history of immune related neurologic disease, multiple sclerosis, autoimmune (demyelinating) neuropathy, Guillain-Barre syndrome, myasthenia gravis; systemic autoimmune disease such as systemic lupus erythematosus (SLE), connective tissue diseases, scleroderma, inflammatory bowel disease (IBD), Crohn's, ulcerative colitis, hepatitis; and patients with a history of toxic epidermal necrolysis (TEN), Stevens-Johnson syndrome, or phospholipid syndrome should be excluded because of the risk of recurrence or exacerbation of disease; patients with rheumatoid arthritis and other arthropathies, Sjogren's syndrome, psoriasis controlled with topical medication, and patients with positive serology, such as antinuclear antibodies (ANA) or anti-thyroid antibodies, should be evaluated for the presence of target organ involvement and potential need for systemic treatment but should otherwise be eligible * Patients 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 (precipitating event) * Patients should be excluded if they have a condition requiring systemic treatment with either corticosteroids or other immunosuppressive medications within 14 days of study drug administration; patients are permitted to use topical, ocular, intra-articular, intranasal, and inhalational corticosteroids (with minimal systemic absorption); a brief course of corticosteroids for prophylaxis (e.g., contrast dye allergy) or for treatment of non-autoimmune conditions (e.g., delayed-type hypersensitivity reaction caused by contact allergen) is permitted * Diagnosis of any second malignancy within the last 5 years prior to cycle 1, day 1, with the exception of those with a negligible risk of metastasis or death, per investigator's discretion (such as adequately treated carcinoma in situ of the cervix, basal or squamous cell skin cancer, localized prostate cancer treated surgically with curative intent, ductal carcinoma in situ treated surgically with curative intent) * Use of live vaccines against infectious disease (e.g. varicella) within 28 days of initiation of study therapy; killed vaccinations (e.g. influenza) are allowed at any appropriate time before and during the study * Life expectancy \< 3 months, per consenting investigator's opinion