Inclusion Criteria:  Histologically confirmed persistent/recurrent endometrial carcinomas. Patients with the following types of endometrial cancer are eligible:  Serous endometrial cancer (p53 IHC must be confirmed to be aberrant, aberrant p53 expression is consistent with mutant TP53) Carcinosarcoma of the endometrium NOTE: For this study, a histological diagnosis of carcinosarcoma must include identifying high grade malignant epithelial and mesenchymal components. The epithelial element must include serous, grade 3 endometrioid, and/or undifferentiated carcinoma (p53 IHC must be confirmed to be aberrant in the high-grade epithelial component, aberrant p53 expression is consistent with mutant TP53). If the epithelial component is grade 3 endometrioid and/or undifferentiated carcinoma, MMR IHC must show retained expression. Patients with known MSI-H tumors are not eligible. Patients with tumors that have known POLE hotspot mutations are not eligible. The mesenchymal component can be homologous or heterologous. Grade 3 Endometrioid and/or undifferentiated carcinoma (p53 IHC must be confirmed to be aberrant, aberrant p53 expression is consistent with mutant TP53; MMR IHC must show retained expression. Patients with known MSI-H tumors are not eligible. Patients with tumors that have known POLE hotspot mutations are not eligible). Patients must have had at least one but no more than three prior regimens for management of endometrial carcinoma (including neoadjuvant/adjuvant chemotherapy).  Patients must have had at least one but no more than three prior regimens for management of endometrial carcinoma (including neoadjuvant/adjuvant chemotherapy).  Chemotherapy administered in conjunction with primary radiation as a radio-sensitizer WILL be counted as a systemic chemotherapy regimen. All chemotherapy must have been completed at least 3 weeks prior to the start of study therapy. Hormonal Therapy will NOT count as prior treatment line. All hormonal therapy for treatment of endometrial cancer must be discontinued at least one week prior to start of study therapy. Have measurable disease based on RECIST 1.1. Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1.  Have adequate laboratory values as defined in the following table:  °Hematologic  Absolute neutrophil count (ANC) ≥1500/μL  Hemoglobin ≥10.0 g/dL  °Renal  Creatinine clearance (CrCL) or estimated Glomerular filtration rate (GFR) CrCL of ≥51 mL/minute estimated using either the Cockcroft-Gault equation, a 24 hour urine test or another validated test as per local practice (e.g., estimated GFR). Estimated CrCL =(140-age [years]) × weight (kg) × 0.85 (140-age [years]) × weight (kg) × 0.85 serum creatinine (mg/dL) × 72  °Hepatic  Total bilirubin ≤1.5 ×ULN (patients with known Gilbert's disease who have bilirubin level ≤ 3 x ULN may be enrolled) AST and ALT ≤3 × ULN (≤5 × ULN for participants with liver metastases) TSH TSH within normal limits. If TSH is not within normal range despite no symptoms of thyroid dysfunction, normal free T4 level is required. Age ≥ 18  A female participant is eligible to participate if she is not pregnant, not breastfeeding, and at least one of the following conditions applies:  Not a woman of childbearing potential (WOCBP) OR A WOCBP who agrees to follow the contraceptive guidance For WOCBP: negative urine or serum pregnancy test is required HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months of registration are eligible for this trial. Patients 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 investigational regimen are eligible for this trial. The participant provides written informed consent for the trial.  Exclusion Criteria:  Has received prior therapy with an anti-PD-, anti-PD-L1 or anti-CTLA-4 agent. Has received prior PARP inhibitor to include but not limited to olaparib, rucaparib, niraparib, talozaporib. Has received prior lenvatinib or other VEGF TKI therapy to include but not limited to lucitinib, cederinib and cabozantonib in combination with anti-PD-1 or anti-PD-L1 therapy. Has participated in a study of an investigational agent and received cancer directed study therapy within 4 weeks prior to start of study treatment. Has received prior radiotherapy within 2 weeks of start of study treatment. Has received a live vaccine within 30 days prior to the first dose of study drugs. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guérin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (eg, FluMist®) are live attenuated vaccines and are not allowed.  Has a diagnosis of immunodeficiency or is 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 study drugs.  Steroids as CT scan contrast premedication is allowed The use of inhaled or topical corticosteroids is allowed The use of mineralocorticoids (e.g., fludrocortisone) for patients with orthostatic hypotension or adrenocortical insufficiency is allowed. Patients with treated brain metastases are eligible if follow-up brain imaging after CNS-directed therapy shows no evidence of progression, and they have been off steroids for at least 4 weeks prior to start of study treatment and remain clinically stable. Has severe hypersensitivity to pembrolizumab and/or olaparib. Has 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. Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis. Uncontrolled intercurrent illness including, but not limited to: ongoing or active infection (except for uncomplicated urinary tract infection), interstitial lung disease or active, noninfectious pneumonitis, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.  Known clinically significant liver disease, including active viral, alcoholic, or other hepatitis; and cirrhosis.  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 unable to swallow orally administered medication and patients with gastrointestinal disorders likely to interfere with absorption of the study medication. Patients with myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML) or with features suggestive of MDS/AML. Patients currently receiving either strong (eg, itraconazole, telithromycin, clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir) or moderate (e.g. ciprofloxacin, erythromycin, diltiazem, fluconazole, verapamil) inhibitors of cytochrome P450 (CYP)3A4 that cannot be discontinued for the duration of the study. The required washout period prior to starting olaparib is 2 weeks. Participant is currently receiving either strong (phenobarbital, enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine and St John's Wort) or moderate (e.g. bosentan, efavirenz, modafinil) inducers of CYP3A4 that cannot be discontinued for the duration of the study. The required washout period prior to starting olaparib is 5 weeks for phenobarbital and 3 weeks for other agents.