Inclusion Criteria:

          1. Patients must have a diagnosis of high grade recurrent ovarian/fallopian tube or
             primary non-mucinous peritoneal cancer

          2. Be willing and able to provide written informed consent for the trial, indicating that
             the patient has been informed of and understands the experimental nature of the study,
             possible risks and benefits, trial procedures, and alternative options

          3. Be >=18 years of age on day of signing informed consent

          4. Patients should be treated with a minimum of 4 cycles of weekly paclitaxel for
             recurrent disease. [Non-platinum-based therapy given for CT/MR documented recurrence
             where further platinum therapy considered unsuitable]

          5. Patients can have had up to 3 prior lines of platinum-based chemotherapy for ovarian
             cancer before starting weekly paclitaxel

          6. Patients must have achieved at least stable disease or response following a minimum of
             four cycles of weekly paclitaxel (measured by CT/MR)

          7. Trial treatment with pembrolizumab must start within 8 weeks after last paclitaxel
             dose

          8. Availability of archival tissue

          9. Patient has disease amenable to biopsy after paclitaxel (baseline biopsy)

         10. Patient is willing to have a biopsy at baseline and before start of the 4th cycle of
             pembrolizumab

         11. Patient has measurable disease based on RECIST v1.1

         12. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1

         13. Willing and able to comply with the protocol for the duration of the study, including
             the treatment plan, investigations required and follow up visits

         14. Demonstrate adequate organ function as defined in the protocol, all screening labs
             should be performed within 10 days of treatment initiation.

         15. Patients of childbearing potential should have a negative urine or serum pregnancy
             test. If the urine test is positive or cannot be confirmed as negative, a serum
             pregnancy test will be required

         16. Patients of childbearing potential must be willing to use an adequate method of
             contraception as outlined in protocol from the start of treatment through to 4 months
             after the last dose of study medication

        Exclusion criteria:

          1. 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 (eg, CTLA-4, OX-40,
             CD137)

          2. Has a diagnosis of low grade or mucinous ovarian cancer

          3. Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy (dose
             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 (n.b. the use of
             physiologic doses of corticosteroids may be approved after consultation with UCL CTC).
             Use of inhaled steroids is permitted.

          4. Has a known history of active TB (Bacillus Tuberculosis)

          5. Has known history of Hepatitis B (defined as Hepatitis B surface antigen [HBsAg]
             reactive) or known Hepatitis C virus (defined as HCV RNA [qualitative] is detected)*

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

          7. Has received prior systemic anti-cancer therapy including investigational agents
             within 4 weeks (could consider shorter interval for kinase inhibitors or other short
             half-life drugs) prior to registration.

             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

          8. 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 (a maximum of 2 weeks radiotherapy is allowed) to non-CNS
             disease

          9. Patients with concurrent or previous malignancy within the last 5 years (except Stage
             I grade 1 endometrial cancer; in situ cervical cancer; DCIS of the breast) that could
             compromise assessment of the primary or secondary endpoints of the trial

         10. Active central nervous system (CNS) metastases and/or carcinomatous meningitis;
             patients with previously treated brain metastases may participate

         11. Has active autoimmune disease that required systemic treatment in past 2 years (i.e.
             with use of disease modifying agents, corticosteroids (at doses >10mg prednisolone
             daily or equivalent) or immunosuppressive drugs) except vitiligo or resolved childhood
             asthma/atopy. Replacement hormone therapy (e.g. levothyroxine, insulin, or physiologic
             corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is
             permitted

         12. Has a corrected serum calcium of >1.5 x ULN despite maximal antihypercalcaemic therapy

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

         14. Has a newly diagnosed venous thrombotic event (e.g. PE, DVT) untreated with
             anticoagulation. Patients must have received at least 14 days of anticoagulation for a
             new thrombotic event and be suitable for continued therapeutic anticoagulation during
             trial participation. Patients are excluded if they have a history of arterial
             thrombosis

         15. Has an active infection requiring systemic therapy

         16. Has symptoms of bowel obstruction in the past three months

         17. Any serious and/or unstable pre-existing medical, psychiatric or other condition that,
             in the treating clinician's judgement could interfere with patient safety or obtaining
             informed consent

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

         19. Is pregnant or breastfeeding, or expecting to conceive children within the projected
             duration of the trial, starting with the screening visit through to 4 months after the
             last dose of trial treatment

         20. Has received a live vaccine within 30 days of planned start of study treatment.
             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.