Trial of Pembrolizumab Following Weekly Paclitaxel for Platinum-resistant Ovarian, Fallopian Tube or Peritoneal Cancer

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. Fresh tumour biopsy should be taken at baseline if this is judged by radiological assessment to be technically feasible. If a biopsy is taken at baseline, then a second biopsy should be taken, if feasible before the start of cycle 4 10. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 11. Willing and able to comply with the protocol for the duration of the study, including the treatment plan, investigations required and follow up visits 12. Demonstrate adequate organ function as defined in the protocol, all screening labs should be performed within 10 days of treatment initiation. 13. 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 14. 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/ interstitial lung disease 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.