CMP-001 in Combination With Pembrolizumab in Subjects With Recurrent or Metastatic Head and Neck Squamous Cell Carcinoma

Inclusion Criteria: * Histologically- or cytologically-confirmed recurrent or metastatic HNSCC considered incurable by local therapies. * No prior systemic therapy in the recurrent or metastatic setting. Systemic therapy as part of multi-modal treatment for locally advanced disease is allowed. * Primary tumor locations of oropharynx, oral cavity, hypopharynx, larynx or paranasal sinus. Participants may not have a primary tumor site of nasopharynx (any histology). * Able to provide tissue from a core or excisional biopsy (fine needle aspirate is not sufficient). A newly obtained biopsy (within 90 days before the start of study treatment) is preferred but an archival sample is acceptable. * Combined Positive Score (CPS) ≥ 1 for PD-L1 on Immunohistochemistry (IHC) of tumor tissue. * Have results of tumor HPV p16 by IHC for oropharyngeal cancer. * Measurable disease as defined by RECIST v1.1, and both of the following: 1. At least 1 lesion amenable to repeated Intratumoral (IT) injection. 2. Documented disease progression in any lesion that was previously radiated in order to serve as a target lesion. * Adequate organ function based on most recent laboratory values within 3 weeks before the first dose of study drug on Week 1 Day 1 (W1D1) Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 to 1 at Screening. * Capable of understanding and complying with protocol requirements. * Women of childbearing potential must have negative serum pregnancy test during Screening and be willing to use an adequate method of contraception from the time of consent until at least 120 days after the last dose of study drug. * Male subjects must be surgically sterile or must agree to use adequate method of contraception from the time of consent until at least 120 days after the last dose of study drug. * Able and willing to provide written informed consent and to follow study instructions. * Subjects unable to provide written informed consent on their own behalf will not be eligible for the study. Exclusion Criteria: * Disease suitable for local therapy administered with curative intent. * Has PD within 3 months of completion of curatively intent systemic treatment for locoregionally advanced HNSCC. * Radiation therapy (or other non-systemic therapy) within 2 weeks before the first dose of study drug on W1D1. * Received prior therapy with PD-1 or PD-L1 blocking antibody therapy in the recurrent/ metastatic setting. If PD-1 or PD-L1 blocking antibody therapy was given as part of curative intent therapy, it must be at least 1 year since receipt of PD-1 or PD-L1 blocking antibody. * Not fully recovered from adverse events (to Grade 1 or less \[per CTCAE v5.0\]), with the exception of persistent alopecia, neuropathy, ototoxicity, hypothyroidism, pain, or dysphagia, due to prior treatment. * Requires systemic pharmacologic doses of corticosteroids greater than the equivalent of 10 mg/day prednisone within 30 days before the first dose of study drug on W1D1. 1. Subjects who are currently receiving steroids at a prednisone-equivalent dose of ≤ 10 mg/day do not need to discontinue steroids prior to enrollment. 2. Replacement doses, topical, ophthalmologic, and inhalational steroids are permitted. * Active pneumonitis, history of noninfectious pneumonitis that required steroids, or history of interstitial lung disease. * Severe uncontrolled cardiac disease within 6 months of Screening, including but not limited to poorly controlled hypertension, unstable angina, myocardial infarction, congestive heart failure (New York Heart Association Class II or greater), pericarditis within the previous 6 months, cerebrovascular accident, implanted or continuous use of a pacemaker or defibrillator. * Known history of immunodeficiency. * Known additional malignancy that is progressing or required active treatment within the past 3 years. Exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin that has undergone potentially curative therapy, curatively treated localized prostate cancer with non-detectable prostate-specific antigen, in situ cervical cancer on biopsy or a squamous intraepithelial lesion on Papanicolaou smear, and thyroid cancer (except anaplastic). * Active autoimmune disease that has required systemic treatment in past 2 years; replacement therapy is not considered a form of systemic treatment * Untreated, symptomatic, or enlarging central nervous system (CNS) metastases or carcinomatous meningitis. * Prior allogenic tissue/solid organ transplant. * Active infection requiring systemic therapy. * Known or suspected active infection with SARS-CoV-2 virus. * Known or suspected infection with human immunodeficiency virus, hepatitis B virus or hepatitis C virus; testing is not required unless suspected. * Received a live virus vaccination within 30 days before the start of study drug dosing on W1D1. * Received blood products (including platelets or red blood cells) or colony stimulating factors \[including granulocyte colony-stimulating factor (GCSF), granulocyte-macrophage colony-stimulating factor (GMCSF) (or recombinant erythropoietin)\] within 30 days before the start of Screening. * Any concurrent uncontrolled illness, including mental illness or substance abuse, which in the opinion of the Investigator, would make the subject unable to cooperate or participate in the trial. * Participation in another clinical trial of an investigational anticancer therapy or device within 30 days before the first dose of study drug. * Requires prohibited treatment (ie. non-protocol specified anticancer pharmacotherapy, surgery or conventional radiotherapy for treatment of malignant tumor). * Has a life expectancy of less than 3 months and/or has rapidly progressing disease (eg. tumor bleeding, uncontrolled tumor pain) in the opinion of the treating Investigator. * Received previous CMP-001 treatment. * Pregnant or breast-feeding or expecting to conceive or father children within the projected duration of the study, from the time of consent until at least 120 days after the last dose of study drug.