Phase II Sequential Treatment Trial of Single Agent Nivolumab, Then Combination Ipilimumab + Nivolumab in Metastatic or Unresectable Non-Clear Cell Renal Cell Carcinoma (ANZUP1602)

Inclusion Criteria: 1. Histologically confirmed unresectable, locally advanced (defined as disease not amenable to curative surgery or radiation therapy) or metastatic nccRCC (both treatment-naïve or those treated with a VEGFR TKI or another systemic medical therapy). Non-clear cell histology including: * Papillary renal cell carcinoma (type 1) * Papillary renal cell carcinoma (type 2) * Other: including chromophobe renal cell carcinoma, pure sarcomatoid renal cell carcinoma, Xp11 translocation (TFE3+ IHC) carcinoma, other renal carcinoma NOS 2. Be ≥18 years of age on the day of signing informed consent 3. At least 1 target lesion according to RECIST v1.1. 4. Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 5. Adequate bone marrow function (should be performed within 14 days prior to registration and with values within the ranges specified below): * Haemoglobin ≥ 90g/L * Platelets ≥ 100x109/L * Neutrophil count ≥ 1.5x109/L 6. Adequate liver function (should be performed within 14 days prior to registration and with values within the ranges specified below): * Bilirubin ≤ 1.5 x upper limit of normal (ULN) except for participants with known Gilbert's syndrome who can have total bilirubin \< 3.0 mg/dL * AST or ALT ≤ 3.0 x ULN (or ≤ 5.0x ULN in the presence of liver metastases) 7. Adequate renal function (should be performed within 14 days prior to registration and with values within the ranges specified below): * Creatinine ≤ 1.5x ULN OR * Creatinine clearance (CrCl) ≥ 30mL/min (use Cockcroft-Gault Formula) 8. Female participants of childbearing potential should have a negative urine or serum pregnancy within 24 hours prior to registering the patient. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. 9. Female participants of childbearing potential should be willing to use two methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through to 5 months after the last dose of study medication. Participants of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year. 10. Male participants should agree to use an adequate method of contraception starting with the first dose of study therapy through to 7 months after the last dose of study therapy. 11. Able to provide a formalin-fixed paraffin embedded (FFPE) tumour block, representative of the participant's primary or metastatic disease (preferred), which must be forwarded to the Centre for Biostatistics and Clinical Trials (BaCT) within 10 working days post registration 12. Willing and able to start treatment within 14 days of registration, and to comply with all study requirements, including the timing and/or nature of the required treatment and assessments 13. Has provided signed, written informed consent. Exclusion Criteria: 1. Urothelial or transitional cell carcinoma of the renal pelvis or ureter 2. Predominant clear cell renal cell carcinoma. A minority of clear cell histology (\<50%) is acceptable, but there must be \>50% non-clear cell histology predominant. 3. Participation in a study of an investigational agent within 30 days of registration. 4. Prior treatment with nivolumab, ipilimumab, or with any other anti-PD-1, anti-PD-L1, Anti-PD-L2, anti-CTLA-4 antibody or any other antibody or drug specifically targeting T cell co-stimulation or immune checkpoint pathways (NB Participant is eligible for Part 2 of the study if they took nivolumab monotherapy in Part 1 of the study). 5. 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. 6. Any condition requiring systemic treatment with either corticosteroids (\>10mg daily prednisone or equivalent dose of alternative corticosteroid) or other immunosuppressive medications within 14 days of registration. Intranasal, inhaled or topical steroids are permitted in the absence of active autoimmune disease. Participants are permitted to enrol 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. 7. Untreated brain or leptomeningeal metastases or current clinical or radiological progression of known brain metastases or requirement for steroid therapy for brain metastases. Participants with treated brain metastases are eligible if they have been stable and off steroids for ≥ 3 weeks. 8. Prior allogeneic organ transplant, inflammatory bowel disease, pneumonitis, tuberculosis, or primary immunodeficiency 9. Active infection requiring systemic therapy within 14 days before registration. 10. Receipt of live attenuated vaccination within 30 days of registration. 11. Life expectancy of less than 3 months. 12. Prior systemic therapy, surgery or radiation therapy within 4 weeks before registration. Note: If the participant has undergone major surgery, they must have recovered adequately before registration. Prior treatments with radiation therapy in the adjuvant and/or metastatic setting is permitted provided that therapy and is completed at least 14 days prior to the first dose of study drug and all treatment related adverse events are \< Grade 1 at the time of registration. 13. History of another active malignancy within the previous 5 years, except for locally curable cancers that have been apparently cured, such as low-grade thyroid carcinoma, prostate cancer not requiring treatment (Gleason grade ≤ 6), basal or squamous cell skin cancer, superficial bladder cancer, melanoma in situ or carcinoma in situ of the prostate, cervix, or breast. Participants who have been free of other malignancies for ≥ 5 years prior to registration are eligible for this study. 14. Positive test for hepatitis B virus surface antigen (HBVsAg) or antibodies to hepatitis C virus ribonucleic acid (HCV antibody) indicating acute or chronic infection. 15. A history of other significant infection, including HIV. HIV testing is not mandatory unless clinically indicated. 16. Participants should be excluded if they have a history of allergy to study drug components, or a history of severe hypersensitivity reaction to any monoclonal antibody. 17. Serious medical or psychiatric conditions that might limit the ability of the patient to comply with the protocol 18. Female patient is pregnant or lactating.