• Patients must have:

‣ A diagnosis of HLRCC with a histologic or cytologic confirmation of RCC consistent with this diagnosis (Cohort 1) OR

⁃ Cytologically or histologically confirmed sporadic/non-HLRCC papillary renal cell carcinoma (presence of papillary component) (Cohort 2)

• Patients must have advanced RCC with 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) by chest x-ray or as \>= 10 mm (\>= 1 cm) with CT scan, MRI, or calipers by clinical exam. To be considered pathologically enlarged and measurable, a lymph node must be \>= 15 mm (\>= 1.5 cm) in short axis

• Patients must have received no more than two prior regimens targeting the VEGF pathway and no prior bevacizumab therapy in the metastatic/advanced setting. No prior treatment with PD-1 or PD-L1 inhibitors in the metastatic/advanced setting. No prior therapy is required for eligibility

• Age \>= 12 years

• Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)

• Absolute neutrophil count \>= 1,000/mcL

• Platelets \>= 100,000/mcL

• Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (\< 3 x upper limit of reference range in patients with known/suspected Gilbert's disease)

• Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional ULN (or =\< 5 x upper limit of reference range if considered to be related to liver or bone metastases by the principal investigator \[PI\])

• Alkaline phosphatase =\< 2.5 x institutional ULN (or =\< 5 x upper limit of reference range if considered to be related to liver or bone metastases by the PI)

‣ Note: For pediatric patients (\< 18 years of age), ULN for alkaline phosphatase will be defined as 390 IU/L for males and 320 IU/L for females

• Glomerular filtration rate (GFR) \>= 30 mL/min/1.73 m\^2

‣ Note: For pediatric patients (\< 18 years of age) the following creatinine thresholds will be utilized. Patients with a creatinine that exceeds this threshold will require further testing with a confirmation of GFR \>= 40 as determined by either 24-hour urine collection or with radioisotope based nuclear medicine evaluation

⁃ Age: 12 to \< 13 years; Maximum serum creatinine (mg/dL): 1.2 (male); 1.2 (female)

∙ The threshold creatinine values in this table were derived from the Schwartz formula for estimating GFR, utilizing child length and stature data published by the Centers for Disease Control and Prevention (CDC)

• Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with an undetectable viral load within 6 months are eligible for this trial

• For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated

• Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load

• Patients with treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression/recurrence for \>= 3 months and the patient no longer requires more than a physiologic dose of steroids

• Patients with a prior or concurrent invasive malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial

• Patients with a known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better

• The effects of study drugs on the developing human fetus are unknown. For this reason, all women and men of childbearing potential must agree to use adequate contraception (including but not limited to abstinence, barrier methods, hormonal contraceptives \[birth control pills, injections, or implants\], intrauterine device \[IUD\], tubal ligation, vasectomy) prior to study entry and for 6 months after completion of study therapy. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, and 6 months after completion of study drugs administration

• Subjects must provide archival tissue block or unstained tumor tissue or be willing to undergo biopsy to collect samples for retrospective central pathology review

• The ability of subject or parent/guardian to understand and the willingness to sign a written informed consent document or subjects with impaired decision making capacity (IDMC) if they are represented by a legally authorized representative (LAR)