Aldesleukin and Pembrolizumab in Treating Patients With Advanced or Metastatic Kidney Cancer

Inclusion Criteria: * Be willing and able to provide written informed consent for the trial * Be \>= 18 years of age on day of signing informed consent * Have histologic confirmation of RCC with a clear cell component * Have advanced (not amenable to potentially curative surgery) or metastatic RCC * May have received previous systemic treatments or regimens for metastatic RCC. Prior therapy can include checkpoint blocking antibodies targeting PD-1, PD-L1, or cytotoxic Tlymphocyte-associated antigen-4 (CTLA-4) and/or targeted agents including TKIs, mTOR inhibitors, or bevacizumab. Patients may choose to receive study treatment as their initial therapy * Previously treated patients must have documented disease progression after their last line of therapy * Have measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Available tissue from an archival tissue sample or newly obtained core or excisional biopsy of a tumor lesion * Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) performance scale * Absolute neutrophil count (ANC) \>= 1,500 /mcL (within 14 days of treatment initiation) * Platelets \>= 100,000/mcL (within 14 days of treatment initiation) * Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L (within 14 days of treatment initiation) * Serum creatinine =\< 1.5 X upper limit of normal (ULN) OR measured or calculated creatinine clearance (glomerular filtration rate \[GFR\] can also be used in place of creatinine or CrCl) \>= 40 mL/min for subject with creatinine levels \> 1.5 X institutional ULN; creatinine clearance should be calculated by Cockcroft-Gault (within 14 days of treatment initiation) * Serum total bilirubin =\< 1.5 X ULN OR direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN (within 14 days of treatment initiation) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) =\< 2.5 X ULN OR =\< 5 X ULN for subjects with liver metastases (within 14 days of treatment initiation) * International normalized ratio (INR) or prothrombin time (PT) =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants (dose level 2 and 3 patients only) (within 14 days of treatment initiation) * Activated partial thromboplastin time (aPTT) =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants (dose level 2 and 3 patients only) (within 14 days of treatment initiation) * Forced expiratory volume in 1 second (FEV1) and forced vital capacity (FVC) \>= 65% of predicted (Testing performed prior to study screening are allowable. Pre-treatment testing must have been completed within 6 months of start of treatment) (within 14 days of treatment initiation) * Left ventricular ejection fraction (LVEF) \>= 50% measured by multigated acquisition (MUGA) scan, echo, or stress test study with myocardial perfusion imaging (Testing performed prior to study screening are allowable. Pre-treatment testing must have been completed within 6 months of start of treatment) (within 14 days of treatment initiation) * Normal/negative cardiac stress testing with myocardial perfusion imaging OR cardiac catheterization with non-significant angiogram findings reviewed by a cardiology consultant (Testing performed prior to study screening are allowable. Pre-treatment testing must have been completed within 6 months of start of treatment) (within 14 days of treatment initiation) * Female subject of childbearing potential should have a negative urine or serum pregnancy test within 72 hours prior to receiving the first dose of study medication; if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 140 days after the last dose of study medication; subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year * Male subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 200 days after the last dose of study therapy Exclusion Criteria: * Has received prior therapy with IL-2 or other investigational systemic cytokine therapy signaling through a common gamma-chain cytokine receptor including IL-7, IL-15 or IL-21 * Is currently participating in or has participated in a study of an investigational agent or using an investigational device within 4 weeks of the first dose of treatment * Has had a prior monoclonal antibody within 4 weeks prior to study day I. Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study day 1 * Adverse events due to prior treatment must be resolved to \< grade 1 \* Note: If subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy * For patients previously treated with checkpoint blocking antibodies, no history of myocarditis, pneumonitis or nephritis of any grade associated with the prior treatment * Has had autoimmune toxicity associated with prior checkpoint blocking antibodies requiring more than one drug class of immune suppressive therapy to resolve (e.g. steroid-refractory toxicity requiring infliximab, mycophenolate mofetil, tacrolimus or other immune suppressive agent) or requiring continuous immune suppression \> 12 weeks, or having a severity judged to be life threatening by the investigator * Has a known additional malignancy that is progressing or requires active treatment; exceptions include locally curable cancers such as basal cell carcinoma of the skin, squamous cell carcinoma of the skin, superficial bladder cancer, or carcinoma in situ of the cervix or breast that has undergone potentially curative therapy * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis * (Dose level 1) subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment * (Dose Level 2 and 3) subjects may not have any history of or current CNS metastases; baseline imaging of the brain is required within 28 days prior to the start of study treatments * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment * Has an active autoimmune disease requiring systemic treatment within the past 3 months or a documented history of clinically severe autoimmune disease, or a syndrome that requires systemic steroids or immunosuppressive agents; subjects with vitiligo or resolved childhood asthma/atopy would be an exception to this rule; subjects that require intermittent use of bronchodilators or local steroid injections would not be excluded from the study; subjects with hypothyroidism stable on hormone replacement or Sjorgen's syndrome will not be excluded from the study * Has history of (non-infectious) pneumonitis that required steroids or active, non-infectious pneumonitis * Ongoing symptomatic cardiac dysrhythmias, uncontrolled atrial fibrillation, or prolongation of the corrected QT interval defined as \> 450 msec for males and \> 470 msec for female * History of any of the following cardiovascular conditions within 6 months of enrollment: cardiac angioplasty or stenting, myocardial infarction, unstable angina, coronary artery bypass graft surgery, class III or IV congestive heart failure as defined by the New York Heart Association, symptomatic peripheral vascular disease, cerebrovascular accident, or transient ischemic attack * Has an active infection requiring systemic therapy * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment * Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies) * Has known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected) * Has received a live vaccine within 30 days prior to the first dose of trial treatment; administration of killed vaccines are allowed; Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed