Study of GSK3359609 and Pembrolizumab in Programmed Death Receptor 1-ligand 1 (PD-L1) Positive Recurrent or Metastatic Head and Neck Squamous Cell Carcinoma

Inclusion Criteria:

* Capable of giving signed informed consent
* Male or female, age \>=18 years
* Histological or cytological documentation of Head and Neck Squamous Cell Carcinoma (HNSCC) that is considered incurable by local therapies
* Primary tumor location of the oral cavity, oropharynx, hypopharynx or larynx
* No prior systemic therapy administered in the recurrent or metastatic setting (except for systemic therapy given as part of multimodal treatment for locally advanced disease)
* Measurable disease per RECIST version 1.1 guidelines
* ECOG Performance PS score of 0 or 1
* Adequate organ function
* Life expectancy of at least 12 weeks
* Female participants: must not be pregnant, not breastfeeding, and at least one of the following conditions apply:

  1. Not a woman of childbearing potential (WOCBP)
  2. A WOCBP who agrees to use a method of birth control from 30 days prior to randomization and for at least 120 days after the last dose of study treatment
* Male participants with female partners of child-bearing potential: must agree to use a highly effective contraception while receiving study treatment and for at least 120 days after the last dose of study treatment and refrain from donating sperm during this period
* Provide tumor tissue from excisional or core biopsy (fine needle aspirates and bone biopsies are not acceptable) acquired within 2 years prior to randomization for PD-L1 immunohistochemistry (IHC) testing by central laboratory
* Have PD-L1 Immunohistochemistry (IHC) CPS 1 status by central laboratory testing
* Have results from testing of Human Papilloma Virus (HPV) status for oropharyngeal cancer

Exclusion Criteria:

* Prior therapy with an anti-PD-1/L1/L2 and/or anti-ICOS directed agent
* Systemic approved or investigational anticancer therapy within 30 days or 5 half-lives of the drug, whichever is shorter
* Major surgery 28 days prior to randomization
* Has high risk of bleeding
* Toxicity related to prior treatment that has not resolved to \<=Grade 1 (except alopecia, hearing loss, endocrinopathy managed with replacement therapy, and peripheral neuropathy which must be\<= Grade 2)
* Received transfusion of blood products or administration of colony stimulating factors within 14 days prior to randomization
* Central nervous system (CNS) metastases, with the following exception: Participants with asymptomatic CNS metastases who are clinically stable and have no requirement for steroids for at least 14 days prior to randomization
* Invasive malignancy or history of invasive malignancy other than disease under study within the last 3 years, except as noted below:

  a. Any other invasive malignancy for which the participant was definitively treated, has been disease-free for 3 years and in the opinion of the principal investigator and GSK Medical Monitor will not affect the evaluation of the effects of the study treatment on the currently targeted malignancy, may be included in this clinical study
* Autoimmune disease or syndrome that required systemic treatment within the past 2 years
* Has a diagnosis of immunodeficiency or is receiving systemic steroids (≥10 mg oral prednisone per day or equivalent) or other immunosuppressive agents within 7 days prior to randomization
* Receipt of any live vaccine within 30 days prior randomization
* Prior allogeneic/autologous bone marrow or solid organ transplantation
* Has current pneumonitis or history of non-infectious pneumonitis that required steroids or other immunosuppressive agents
* Recent history (within the past 6 months) of uncontrolled symptomatic ascites, pleural or pericardial effusions
* Recent history (within the past 6 months) of gastrointestinal obstruction that required surgery, acute diverticulitis, inflammatory bowel disease, or intra-abdominal abscess
* Recent history of allergen desensitization therapy within 4 weeks of randomization
* History or evidence of cardiac abnormalities within the 6 months prior to randomization
* Cirrhosis or current unstable liver or biliary disease per investigator assessment defined by the presence of ascites, encephalopathy, coagulopathy, hypoalbuminemia, esophageal or gastric varices, or persistent jaundice
* Active infection requiring systemic therapy
* Known HIV infection, or positive test for hepatitis B active infection (presence of hepatitis B surface antigen), or hepatitis C active infection
* History of severe hypersensitivity to monoclonal antibodies or any ingredient used in the study treatment formulations
* Known history of active tuberculosis
* Any serious and/or unstable pre-existing medical (aside from malignancy), psychiatric disorder, or other condition that could interfere with participant's safety, obtaining informed consent, or compliance to the study procedures in the opinion of the investigator
* Is currently participating in (unless in follow-up phase and 4 weeks have elapsed from last dose of prior investigational agent), or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to date of randomization
* Pregnant, breastfeeding, or expecting to conceive or father children within the projected duration of the study