You can participate in this study if you:

• Subject (or legally acceptable representative, if applicable) provides written informed consent for the study.
• Subject is greater than or equal to 18 years of age on the day of signing the informed consent.
• Have a history of histologically- or cytologically-confirmed diagnosis of recurrent and/or metastatic squamous cell cancer of the head and neck (HNSCC)
• For female subjects defined as women of childbearing potential (WOCBP), a negative urine pregnancy test must be obtained during screening. If the urine test cannot be confirmed as negative, a serum pregnancy test will be required. Women who are surgically sterile or at least 2 years postmenopausal do not require pregnancy testing.
• Male subjects of childbearing potential must agree to use a condom as an effective method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy.

You cannot participate in this study if you:

• Primary tumor location of nasopharynx (any histology).
• If the urine pregnancy test is positive. If the urine test cannot be confirmed as negative, a serum pregnancy test will be required.
• Has received prior therapy with HPV-specific immunotherapy including therapeutic cancer vaccines and cellular immunotherapy. Note: subjects who have received prophylactic HPV vaccines are eligible for enrollment.
• Has received 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 including but not limited to CTLA-4, OX40, CD137.
• Has had major surgery, including surgical resection of tumor, within 30 days prior to randomization, and has not fully recovered as assessed by the investigator.
• Has received a live vaccine within 30 days prior to randomization.
• Has received immunomodulatory or immunosuppressive agents (e.g., interferons (IFNs), tumor necrosis factor, interleukins, immunoglobulins or other biological response modifiers (granulocyte colony-stimulating factor [GCSF] or granulocyte macrophage stimulating factor [GMCSF]) within 30 days prior to randomization.
• Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 30 days prior to randomization.
• Has undergone prior allogeneic hematopoietic stem cell transplantation within the last 5 years. Note: Subjects who have had a transplant greater than 5 years ago are eligible as long as there are no symptoms of graft- versus-host disease [GVHD].
• Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (I a dose exceeding 10 mg daily of prednisone equivalent). Note: Current or recent use of intranasal, intra-articular, and topical steroids are allowed for symptom management are clinically indicated.
• Has known carcinomatous meningitis and/or active central nervous system (CNS) metastases as defined by new brain metastases or progressive brain metastases that have not been subjected to CNS-directed therapy since documented progression.
• Has a history of hepatitis B (HBV) infection or known to be positive for HBV antigen (HbsAg)/HBV virus DNA.
• Female subjects defined as WOCBP unwilling or unable to use highly effective contraception method(s) for the duration of the study
• History of allergic or hypersensitivity reactions (greater than or equal to Grade 3) to pembrolizumab, PDS0101, or their excipients.