Belzutifan in Recurrent Clear Cell Carcinoma of Gynecologic Origin

Inclusion Criteria: * Participants must have histologically or cytologically confirmed recurrent or persistent clear cell carcinoma of the ovary (CCOC) or clear cell carcinoma of other gynecologic origin (e.g., endometrial, cervical, vaginal, vulvar, endometriosis-related). If mixed histology, then ≥50% clear cell component. * Participants must have measurable disease, defined as at least one lesion that can be accurately measured per Response Evaluation Criteria in Solid Tumors (RECIST) v1.1 criteria. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. * Participants must have received at least one prior platinum-based chemotherapeutic regimen for primary management of disease. * Prior bevacizumab is allowed. * Prior use of immunotherapy is allowed. * Unlimited prior lines for the treatment of recurrent or persistent disease are allowed. * Age ≥18 years. Because no dosing or adverse event data are currently available on the use of Belzutifan in participants \<18 years of age, children are excluded from this study. * ECOG (Eastern Cooperative Oncology Group) performance status of 0 or 1 (Karnofsky performance scale ≥70%, see Appendix A). * Participants must meet the following organ and marrow function as defined below: * Absolute neutrophil count ≥ 1,500/mcL * Hemoglobin ≥ 10.0 g/dL (without use of erythropoietin; without packed red blood cell (RBC) transfusion within preceding 2 weeks) * Platelets ≥ 100,000/mcL * Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN) OR direct bilirubin ≤ ULN for participants with total bilirubin levels \> 1.5 ULN * AST(SGOT)/ALT(SGPT) ≤ 2.5 × institutional upper limit of normal (ULN) (in the absence of liver metastases) or ≤ 5 x institutional ULN (in the presence of liver metastases) * Creatinine ≤ 1.5 x institutional upper limit of normal (ULN) OR estimated creatinine clearance (CrCl) by the Cockcroft-Gault formula ≥51mL/min if creatinine \> 1.5 x institutional ULN or institutional standard method * INR OR PT and PTT ≤1.5 × institutional ULN unless participant is receiving anticoagulant therapy and PT/INR or PTT are within therapeutic range of that anticoagulation * Participants with known brain metastases are eligible if they have completed primary CNS-directed therapy (such as surgical resection or radiotherapy) and if they have remained clinically stable, asymptomatic, radiologically stable without evidence of progression for at least 4 weeks by repeat imaging and have been off of steroids for at least 4 weeks prior to starting study treatment. * Participants with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the Belzutifan, as determined after discussion with the Sponsor-Investigator, are eligible for this trial. * Archival tumor tissue must be available as 17 (15 unstained + 2 H\&E) freshly serially cut slides from formalin-fixed, paraffin-embedded (FFPE) tissue blocks. The most recent available tissue is preferred to archived tissue. If fewer than 17 slides are available, the participant may still be eligible pending discussion with the Sponsor-Investigator. * The effects of Belzutifan on the developing human fetus are unknown. For this reason, women of child-bearing potential\* must have a negative serum or urine pregnancy test at the Screening and Cycle 1 Day 1 visits. A negative serum or urine pregnancy test must be obtained within 24 hours before the first dose of study intervention in order to start receiving the study drug. Women of child-bearing potential and men must agree to use adequate contraception (see Appendix D) prior to study entry, for the duration of study participation, and for at least 30 days after last receipt of study therapy. Additionally, should a woman become pregnant or suspect she is pregnant while she is participating in this study, she should inform her treating physician immediately. --Female participants who do not meet the definition of women of child-bearing potential must meet either criteria: * Post-menopausal, defined as amenorrheic for at least 12 consecutive months within the appropriate age group and without an alternative medical cause OR * Surgically sterilized (i.e. bilateral oophorectomy, bilateral tubal ligation or salpingectomy, or total hysterectomy) * Ability to swallow orally administered medications. * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Prior use of Belzutifan or another HIF-2a inhibitor. * Participant has any of the following: * Pulse oximeter reading \<92% at rest, or * Requires intermittent supplemental oxygen, or * Requires chronic supplemental oxygen * Anti-cancer treatment (chemotherapy, radiotherapy, or other investigational therapy) within 4 weeks prior to entering the study (6 weeks prior to study entry for nitrosoureas or mitomycin C). * Prior small molecule kinase inhibitor (including investigational kinase inhibitor) ≤ 2 weeks prior to entering the study. * Prior radiation therapy within 2 weeks of start of study drugs. Participants must have recovered from all radiation-related toxicities and must not require steroids. Participants must not have had radiation pneumonitis. Palliative radiation (≤2 weeks of radiotherapy) to non-CNS (central nervous system) disease is permitted, provided there is at least a 1-week washout prior to start of study drugs. * Use of herbal supplements, including but not limited to: cannabis, St. John's wort, gingko biloba, ginseng, saw palmetto, and ephedra. Herbal supplements must be stopped at least 1 week prior to beginning study treatment. * Participants who are known to require concomitant therapy with moderate or strong CYP3A4 inducers. Due to potential drug interactions, concomitant use of these medications is not permitted for the duration of treatment on trial. Participants are eligible for study entry if an appropriate substitution is made prior the first dose of study medication. * Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks before the first dose of study intervention. Note: Participants who have entered the follow-up phase of an investigational study may participate as long as it has been 4 weeks after the last dose of the previous investigational agent. * Participants who have AEs due to previous anticancer therapies must have recovered to * Grade 1 or baseline with the exception of alopecia. Participants with endocrine-related AEs who are adequately treated with hormone replacement or participants who have * Grade 2 neuropathy are eligible. * Has received a live or live-attenuated vaccine within 30 days prior to the first dose of study drug. Administration of killed vaccines are allowed. Note: Any licensed COVID-19 vaccine (including for Emergency Use) in a particular country is allowed in the study as long as they are mRNA vaccines, replication-incompetent adenoviral vaccines, or inactivated vaccines. These vaccines will be treated just as any other concomitant therapy. * Major surgical procedures within 4 weeks of beginning study treatment are not allowed. Minor surgical procedures (with the exception of port placement) within 1 week of beginning study treatment are not allowed. * Any gastrointestinal disorder that would interfere with the passage or absorption of oral medications. Participants must be able to swallow oral medications. Participants with an enteric tube (e.g., gastrostomy or jejunostomy tube), receiving total parenteral nutrition (TPN), or dependent on IV fluid support are ineligible. * Participants with significant cardiovascular impairment, including uncontrolled hypertension, congestive heart failure of New York Heart Association Grade II or above, unstable angina, myocardial infarction within the past 6 months, or serious cardiac arrhythmia within the past 6 months. * Has moderate to severe hepatic impairment (Child-Pugh B or C). * Has received colony-stimulating factors (e.g., G-CSF, GM-CSF, or recombinant EPO) ≤28 days prior to the first dose of study intervention. * Has a diagnosis of immunodeficiency. * Is known to be positive for Human Immunodeficiency Virus (HIV). Subjects with HIV, including those on antiretroviral therapy, are excluded due to risk of immunodeficiency and risk of overlapping toxicity. * Is known to be positive for Hepatitis B virus (HBV) or Hepatitis C virus (HCV). Participants are eligible if they have a history of HCV infection that has been treated and cured, with an undetectable viral load. * Participants with uncontrolled intercurrent illness, including but not limited to active infection and serious non-healing wounds or ulcers. * Participants with psychiatric illness/social situations that would limit compliance with study requirements. * Participants with a history of allergic reactions or hypersensitivity attributed to compounds of similar chemical or biological composition to belzutifan. * Pregnant women are excluded from this study. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with belzutifan, breastfeeding participants are excluded from this study. * History or current evidence of any condition, therapy, laboratory abnormality, or other circumstance that might confound the results of the study, interfere with the participant's participation for the full duration of the study, such that it is not in the best interest of the participant to participate, in the opinion of the treating investigator.