Pembrolizumab With or Without Axitinib for Clear Cell Kidney Cancer in Patients Undergoing Surgery

Inclusion Criteria: 1. Histologically confirmed RCC with a clear cell component. 2. Locally advanced or metastatic disease (primary intact or status post nephrectomy with recurrent disease) 3. Planned CN and/or MET. 4. Must have a tumor lesion amenable to biopsy at pre-treatment and subjects must consent to acquisition of fresh tumor specimens obtained using the following approaches: 1. Core biopsy. 2. Nephrectomy. 3. Metastasectomy (MET). Note: Subjects who undergo nephrectomy or metastasectomy prior to study enrollment must still have measurable disease (RECIST 1.1) that is amenable to cytoreductive nephrectomy or metastasectomy to be eligible for study participation. 4. Fine needle aspiration (FNA) specimens are not acceptable. 5. Measurable disease per RECIST 1.1 as assessed by the investigator. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. 6. Subject (or legally acceptable representative if applicable) must provide written informed consent for the trial. 7. At least 18 years of age on day of signing informed consent. 8. Performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) Performance Scale. 9. Adequate organ function as defined in Table 1; all screening labs should be performed within 10 days of treatment initiation. 1. Absolute neutrophil count (ANC) \>= 1,500/microliter (uL) 2. Platelets \>= 100,000/uL. 3. Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L without transfusion or erythropoietin (EPO) dependency (within 7 days of assessment). 4. Serum creatinine =\< 1.5 x upper limit of normal (ULN) OR measured or calculated creatinine clearance (CrCl) (glomerular filtration rate (GFR) can also be used in place of creatinine or CrCl) \>= 60 mL/min for subject with creatinine levels \> 1.5 x institutional ULN. Creatinine clearance should be calculated per institutional standard. 5. Serum total bilirubin =\< 1.5 x ULN OR direct bilirubin =\< ULN for participants with total bilirubin levels \> 1.5 ULN. 6. Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase (SGOT)) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase (SGPT)) =\< 2.5 x ULN. 7. Albumin \>= 2.5 mg/dL. 8. International normalized ratio (INR) or prothrombin time (PT) =\< 1.5 x ULN unless subject is receiving anticoagulant therapy as long as PT or activated partial thromboplastin time (aPTT) is within therapeutic range of intended use of anticoagulants. 9. Activated partial thromboplastin time (aPTT) =\< 1.5 x ULN unless subject is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants (within 10 days of treatment initiation) 10. Negative urine or serum pregnancy test within 72 hours prior to receiving the first dose of study medication (day 1) (female participants of childbearing potential). If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required 11. Male and female participants of childbearing potential must be willing to use an adequate method of contraception\* for the course of the study through 120 days after the last dose of study medication. \* Note: Abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject Exclusion Criteria: 1. RCC WITHOUT a clear cell component. 2. Prior systemic therapy for the treatment of RCC. 3. No measurable disease (e.g. only bone metastases). 4. Not a candidate for CN and/or MET. 5. Currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to the first dose of study treatment. \* Note: Participants who have entered the follow-up phase of an investigational study may participate as long as it has been 4 weeks since the last dose of the previous investigational agent 6. Diagnosis of immunodeficiency or receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment. 7. Known history of active Bacillus tuberculosis (TB). 8. Severe hypersensitivity (\>= grade 3) to pembrolizumab/axitinib or any of their excipients. 9. Prior systemic anti-cancer monoclonal antibody (mAb), targeted small molecule therapy, or radiation therapy within 2 weeks prior to the first dose of study treatment (Day 1). * Note: Participants must have recovered from all adverse events (AEs) due to previous therapies to =\< grade 1 or baseline. Participants with =\< grade 2 neuropathy may be eligible. * Note: If subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study treatment. * Participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. A 1-week washout is permitted for palliative radiation (=\< 2 weeks of radiotherapy) to non-central nervous system (CNS) disease. 10. Known additional malignancy that is progressing or has required active treatment within the past 2 years. \* Note: Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or carcinoma in situ (e.g., breast carcinoma, cervical cancer in situ) that have undergone potentially curative therapy are not excluded 11. Known active CNS metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable, i.e., without evidence of progression for at least 4 weeks by repeat imaging (note that the repeat imaging should be performed during study screening), clinically stable and without requirement of steroid treatment for at least 14 days prior to first dose of study treatment. This exception does not include carcinomatous meningitis, which is excluded regardless of clinical stability. 12. Active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment and is allowed. 13. History of (non-infectious) pneumonitis that required treatment with steroids or has current pneumonitis. 14. Active infection requiring systemic therapy. 15. Any arterial thromboembolic events, including but not limited to myocardial infarction, transient ischemic attack, cerebrovascular accident, or unstable angina, within 6 months prior to randomization. 16. Uncontrolled or poorly controlled hypertension despite standard medical therapy. 17. Serious or nonhealing wound, ulcer, or bone fracture within 28 days of study enrollment. 18. 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. 19. Known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial 20. 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. 21. Any prior therapy with an anti-PD-1, anti-PD-L1,or anti-PD-L2 agent or with an agent directed to another stimulatory or co-inhibitory T cell receptor (e.g., cytotoxic T-lymphocyte-associated protein 4 (CTLA-4), OX-40, CD137). 22. Known history of human immunodeficiency virus (HIV) infection. No HIV testing is required unless mandated by local health authority. 23. Known history of hepatitis B (defined as hepatitis B surface antigen reactive) or known active hepatitis C virus (defined as hepatitis C virus (HCV) ribonucleic acid (RNA) \[qualitative\] is detected) infection. No testing for hepatitis B and hepatitis C is required unless mandated by local health authority. 24. Live vaccine within 30 days prior to the first dose of study drug. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guerin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist) are live attenuated vaccines and are not allowed. 25. History of grade 3-4 gastrointestinal (GI) bleeding within 12 weeks prior to study enrollment. 26. Solid organ or hematologic transplant. 27. Encephalopathy in the last 6 months. Those participants on rifaximin or lactulose to control their encephalopathy are not allowed. 28. Evident ascites on physical examination. * Note: Medically controlled ascites and ascites detectable on imaging studies only is allowed 29. Female of childbearing potential who has a positive urine pregnancy test within 72 hours prior to allocation. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. 30. Has had an allogenic tissue/solid organ transplant.