Study of PDS0101 and Pembrolizumab Combination I/O in Subjects With HPV16 + Recurrent and/or Metastatic HNSCC

Inclusion Criteria: * The participant (or legally acceptable representative if applicable) provides written informed consent for the study. * Be ≥18 years of age on the day of signing the informed consent. * Checkpoint-naïve subjects: Have a history of histologically- confirmed diagnosis of squamous cell cancer of the head and neck (HNSCC) that is recurrent, metastatic, or persistent with: * Confirmed HPV16 infection * Confirmed tumor PDL1 expression defined as a combined positive score (CPS) ≥1 using the FDA-approved Dako PD-L1 immunohistochemistry (IHC) 22C3 PharmDx Assay. * No prior receipt of any immunological therapy for metastatic disease. * Checkpoint experienced subjects have a history of histologically-confirmed diagnosis of HNSCC that is recurrent, metastatic, or persistent with: * Confirmed HPV16 infection * Characterization of tumor PDL1 expression using the FDA-approved PD-L1 IHC 22C3 PharmDx Assay. * Receipt of prior treatment with checkpoint inhibitors as a single agent or in combination, and have received at least 2 doses of the agent or a minimum of 6 weeks on treatment * Have documented clinical progression or recurrence that has been radiologically confirmed * Have recurrent and/or metastatic measurable disease based on RECIST 1.1 as assessed by the local PI/radiology. There must be confirmation that the subject's imaging shows at least 1 lesion that is appropriate for selection as a target lesion per RECIST 1.1. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. * Have adequate organ function as defined in Hematological: ANC ≥1500/μL, Platelets ≥100 000/μL; Hemoglobin ≥9.0 g/dL or ≥5.6 mmol/L; Renal: Creatinine ≤1.5 × ULN measured or calculated creatinine clearance \>30mL/min with creatinine levels or \>1.5 × institutional ULN; Hepatic: Total bilirubin ≤1.5 × ULN or direct bilirubin ≤ULN for subjects with total bilirubin levels \>1.5 × ULN, AST and ALT ≤2.5 ULN (5 × ULN for subjects with liver metastases); Coagulation: INR, PTT ≤1.5 × ULN. Specimens must be collected within 10 days prior to the start of study combination treatment. * If subject received major surgery or radiation therapy of \>30 Gy, they must have recovered from the toxicity and/or complications from the intervention. * For female subjects defined as women of childbearing potential (WOCBP), a negative urine pregnancy test must be obtained during screening. Women who are surgically sterile or at least 2 years postmenopausal do not require pregnancy testing. Note: Female subjects of childbearing potential must be willing to use an effective method of contraception for the course of the study through 120 days after the last dose of study medication. * 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. * Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. Exclusion Criteria: * Pregnancy Exclusion: A female subject defined as a WOCBP who has a positive urine pregnancy test (within 72 hours) prior to treatment. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. * 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 (e.g. CTLA-4, OX40, CD137) and was discontinued from that treatment due to a Grade 3 or higher AE. * Has received prior systemic anti-cancer therapy including investigational agents within 30 days prior to treatment. Note: Subjects must have recovered from all AEs due to previous therapies to ≤Grade 1 or baseline. Subjects with ≤Grade 2 neuropathy and ≤Grade 2 alopecia are an exception to this criterion and may qualify for therapy. Note: If participant received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting treatment. * Has received prior radiotherapy within 2 weeks of start of study treatment. Subjects 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- CNS disease. * Coordination and timing of coronavirus disease 2019 (COVID-19) vaccination should be based on local investigator clinical assessment and judgment. Note: Whenever possible, it is recommended to avoid COVID vaccination on the day of PDS0101 and/or pembrolizumab dosing because it may be difficult to attribute certain AEs (eg, fever, infusion reaction) to the study drug(s) or the COVID vaccine if they are both administered on the same day. * Has received a live vaccine within 30 days prior to the first dose of 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-Guerin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g. FluMist®) are live attenuated vaccines and are not allowed. * Received immunotherapy/immunomodulatory or immunosuppressive agents (e.g. IFNs, tumor necrosis factor, interleukins, immunoglobulins or other biological response modifiers \[GM-CSF, granulocyte colony-stimulating factor, macrophage colony- stimulating factor\]) within 6 weeks prior to administration of the first study combination treatment. * 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 the first dose of study treatment. Note: Subjects who entered the follow-up phase of an investigational study may participate as long as it has been 30 days after the last dose of the previous investigational agent. * Has undergone prior allogeneic hematopoietic stem cell transplantation within the last 5 years. (Subjects 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 (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. Current or recent use of physiologic doses of intra-articular, topical, or inhaled corticosteroids is acceptable. * Has a known additional malignancy that is progressing or has required active treatment within the past 3 years. Note: Subjects with basal cell carcinoma of the skin, squamous cell carcinoma of the skin or carcinoma in situ (eg, breast carcinoma, cervical cancer in situ) or other malignant tumors that have undergone potentially curative therapy are not excluded. * Has known active central nervous system (CNS) metastases and/or carcinomatosis meningitis. Subjects 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 repeat imaging should be performed during study screening clinical stable and without requirement of steroid treatment for at least 14 days prior to first dose of study treatment). * Has severe hypersensitivity (≥Grade 3) to pembrolizumab and/or any of its excipients. * Has an 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 (e.g. thyroxine, insulin or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not consider a form of systemic treatment and is allowed. * Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis. * Has an active infection requiring systemic therapy. * Subjects with known HIV and/or history of Hepatitis B or C infections or known to be positive for Hepatitis B antigen (HBsAg)/Hepatitis B virus (HBV) DNA or Hepatitis C Antibody or RNA. Active Hepatitis C is defined by a known positive Hep C Ab result and known quantitative HCV RNA results greater than the lower limits of detection of the assay. * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the participant's participation for the full duration of the study, or is not in the best interest of the participant to participate, in the opinion of the treating Investigator. * Has a known psychiatric or substance abuse disorder that would interfere with the subject's ability to cooperate with the requirements of the study. * 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 any study treatment. * Has had an allogenic tissue/solid organ transplant. * Has received administration of colony-stimulating factors (including G-CSF, GM-CSF or recombinant erythropoietin) within 30 days prior to Day 1. * Has a history of interstitial lung disease. * Female subjects defined as WOCBP unwilling or unable to use highly effective contraception method(s) for the duration of the study: * Combined (estrogen and progestogen containing) hormonal contraception associated with inhibition of ovulation. * Progestogen-only hormonal contraception * Intrauterine device * Intrauterine hormone-releasing system * Bilateral tubal occlusion * Vasectomized partner is a highly effective birth control method provided that partner is the sole sexual partner of the WOCBP trial participant and that the vasectomised partner has received medical assessment of the surgical success. * Any prior Grade ≥3 immune-related adverse event(irAE) while receiving any previous checkpoint inhibitor or immunotherapy agent, or any unresolved irAE \>Grade 1 except for endocrine AEs managed with replacement therapy. * Developed immune-related toxicity while on prior checkpoint inhibitor therapy that has not yet returned to Grade 1 or better. * History of any drug allergies or significant adverse reactions to any of the components of PDS0101