Inclusion Criteria:

          1. Female participants who are at least 18 years of age on the day of signing informed
             consent with histologically confirmed diagnosis of locally advanced or metastatic
             cervical cancer will be enrolled in this study.

          2. Patients with progression or intolerance to at least one line of therapy in the
             locally advanced or metastatic setting will be eligible for this study.

          3. A female participant is eligible to participate if she is not pregnant, not
             breastfeeding, and at least one of the following conditions applies:

               1. Not a woman of childbearing potential (WOCBP) as defined OR

               2. A WOCBP who agrees to follow the contraceptive guidance during the treatment
                  period and for at least 120 days after the last dose of study treatment.

          4. The participant (or legally acceptable representative if applicable) provides written
             informed consent for the trial.

          5. Have measurable disease based on RECIST 1.1. Lesions situated in a previously
             irradiated area are considered measurable if progression has been demonstrated in such
             lesions.

          6. Have provided archival tumor tissue sample or newly obtained core or excisional biopsy
             of a tumor lesion not previously irradiated. Formalin-fixed, paraffin embedded (FFPE)
             tissue blocks are preferred to slides. Newly obtained biopsies are preferred to
             archived tissue. Note: If submitting unstained cut slides, newly cut slides should be
             submitted to the testing laboratory within 14 days from the date slides are cut.

          7. Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1.
             Evaluation of ECOG is to be performed within 28 days prior to the date of treatment
             initiation.

          8. Have adequate organ function as defined. Specimens must be collected within 28 days
             prior to the start of study treatment.

               1. Absolute neutrophil count (ANC) ≥1500/µL

               2. Platelets ≥100 000/µL

               3. Hemoglobin ≥9.0 g/dL

               4. Creatinine OR Measured or calculated creatinine clearance (GFR can also be used
                  in place of creatinine or CrCl) ≤1.5 × ULN OR ≥30 mL/min for participant with
                  creatinine levels >1.5 × institutional ULN

               5. Total bilirubin ≤1.5 ×ULN OR direct bilirubin ≤ULN for participants with total
                  bilirubin levels >1.5 × ULN

               6. AST (SGOT) and ALT (SGPT) ≤2.5 × ULN (≤5 × ULN for participants with liver
                  metastases)

               7. International normalized ratio (INR) OR prothrombin time (PT), Activated partial
                  thromboplastin time (aPTT) ≤1.5 × ULN unless participant is receiving
                  anticoagulant therapy as long as PT or aPTT is within therapeutic range of
                  intended use of anticoagulants

        Exclusion Criteria:

          1. A WOCBP who has a positive urine pregnancy test within 72 hours prior to treatment
             initiation. If the urine test is positive or cannot be confirmed as negative, a serum
             pregnancy test will be required.

          2. Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti PD L2 agent.

          3. Has received prior systemic anti-cancer therapy including investigational agents
             within 4 weeks Note: Participants must have recovered from all AEs due to previous
             therapies to ≤Grade 1 or baseline. Participants with ≤Grade 2 neuropathy may be
             eligible.Note: If participant received major surgery, they must have recovered
             adequately from the toxicity and/or complications from the intervention prior to
             starting study treatment.

          4. Has received prior radiotherapy within 2 weeks of start of 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.

          5. Has received a live vaccine or live attenuated vaccine within 30 days prior to the
             first dose of study drug. Administration of killed vaccines is allowed.

          6. Is 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.

          7. 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 drug.

          8. Has a known additional malignancy that is progressing or has required active treatment
             within the past 3 years. Note: Participants with basal cell carcinoma of the skin,
             squamous cell carcinoma of the skin, or carcinoma in situ (e.g. breast carcinoma) that
             have undergone potentially curative therapy are not excluded.

          9. Has 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.

         10. Has severe hypersensitivity (≥Grade 3) to pembrolizumab or lenvatinib and/or any of
             their excipients.

         11. 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 (eg. thyroxine, insulin, or physiologic corticosteroid
             replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a
             form of systemic treatment.

         12. Has a history of (non-infectious) pneumonitis/interstitial lung disease that required
             steroids or has current pneumonitis/interstitial lung disease.

         13. Has an active infection requiring systemic therapy.

         14. Has a known history of Human Immunodeficiency Virus (HIV).

         15. Has a known history of Hepatitis B (defined as Hepatitis B surface antigen [HBsAg]
             reactive) or known active Hepatitis C virus (defined as HCV RNA [qualitative] is
             detected) infection. Note: no testing for Hepatitis B and Hepatitis C is required
             unless mandated by local health authority.

         16. Has a history or current evidence of any condition, therapy, or laboratory abnormality
             that might confound the results of the study, interfere with the subject's
             participation for the full duration of the study, or is not in the best interest of
             the subject to participate, in the opinion of the treating investigator.

         17. Has known psychiatric or substance abuse disorders that would interfere with
             cooperation with the requirements of the trial.

         18. Is pregnant or breastfeeding, or expecting to conceive or father children within the
             projected duration of the study, starting with the screening visit through 120 days
             after the last dose of trial treatment.

         19. Has uncontrolled blood pressure (BP) (Systolic BP>140 mmHg or diastolic BP>90 mmHg) in
             spite of an optimized regimen of antihypertensive medication.

         20. Has electrolyte abnormalities that have not been corrected.

         21. Has significant cardiovascular impairment: history of congestive heart failure greater
             than New York Heart Association (NYHA) Class II, unstable angina, myocardial
             infarction or stroke within 6 months of the first dose of study drug, or cardiac
             arrhythmia requiring medical treatment at Screening.

         22. Has bleeding or thrombotic disorders or subjects at risk for severe hemorrhage. The
             degree of tumor invasion/infiltration of major blood vessels (e.g. carotid artery)
             should be considered because of the potential risk of severe hemorrhage associated
             with tumor shrinkage/necrosis following lenvatinib therapy.

         23. Subjects having > 1+ proteinuria on urine dipstick testing unless a 24-hour urine
             collection for quantitative assessment indicates that the urine protein is <1 g/24
             hours.

         24. Has gastrointestinal malabsorption, gastrointestinal anastomosis, or any other
             condition that might affect the absorption of lenvatinib.

         25. Prolongation of QTc interval to >480 ms.