CUE-101with Pembrolizumab for LA-HPV+HNSCCs

Inclusion Criteria: * Participants must have histologically or cytologically confirmed new diagnosis of locally advanced, non-metastatic, head and neck squamous cell carcinoma of the oropharynx (cT1-4 N0-N3 M0) * Participants must be deemed unresectable by a head and neck surgeon for one or more of the following reasons: 1. Inability to obtain a R0 resection with a minimally invasive surgical approach, such as Transoral Robotic Surgery (TORS) 2. Risk of significant functional deficit with a surgical treatment approach 3. Other anatomical (such as retropharyngeal location of the carotid artery) or tumor characteristics that in the surgeon's judgment would be a contra-indication to a minimally invasive surgical approach. * Participants with newly diagnosed HNSCC who underwent partial surgical resection and have gross residual disease are eligible for the study if additional treatment is required. * Participant must have a tumor that is HPV-16 positive and express p16INK4A. Archival tissue or formalin fixed, paraffin-embedded (FFPE) tissue from a biopsy and/or surgery must be available for HPV-16 and p16INK4A testing on all participants enrolled. All tumors must test positive for HPV-16 using ISH analysis or using HPV16 specific PCR testing and p16INK4A expression in tumor cells using IHC analysis. * Archival tissue or formalin fixed, paraffin-embedded (FFPE) tissue from a biopsy and/or surgery must be available for PD-L1 staining. Tumors must be scored for CPS. * Participants must have HLA-A\*0201 genotype as determined by genomic testing. * Participants must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as ≥20 mm (≥2 cm) by chest x-ray or as ≥10 mm (≥1 cm) for non-nodal lesions and \> 15mm (\>1.5 cm) for nodal lesions with CT scan, magnetic resonance imaging (MRI), or calipers by clinical exam. See section 11 (Measurement of Effect) for the evaluation of measurable disease. * Age ≥18 years. Since no dosing or adverse event data are currently available on the use of CUE-101 alone or in combination with pembrolizumab in participants \<18 years of age, children are excluded from this study. * ECOG performance status of 0 or 1 (Karnofsky ≥60%, see Appendix A). * Participants must have adequate organ and marrow function as defined below in the protocol * Human immunodeficiency virus (HIV)-infected participants on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial. * For participants with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. * Participants with a history of hepatitis C virus (HCV) infection must have been treated and cured. For participants with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load. * Participants with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. * Participants with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, participants should be class 2B or better. * A male participant must agree to use of a highly effective method of contraception during the treatment period and for at least 120 days after the last dose of study treatment and refrain from donating sperm during this period. * A female participant is eligible to participate if she is not pregnant, not breastfeeding, and at least one of the following conditions applies: 1. Not a woman of childbearing potential (WOCBP) as defined as any female who has experienced menarche and who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy) or is not postmenopausal or 2. A WOCBP who agrees to follow the contraceptive guidance during the treatment period and for at least 120 days after the last dose of study treatment. 3. Highly effective methods of contraception: i. Combined (estrogen and progestogen containing) hormonal contraception associated with inhibition of ovulation: oral, intravaginal, or transdermal. ii. Progestogen-only hormonal contraception associated with inhibition of ovulation: oral, injectable, or implantable. iii. Non-hormonal (copper) intrauterine device. iv. Intrauterine hormone-releasing system. v. Bilateral tubal occlusion/ligation. vi. Sexual abstinence, i.e., refraining from heterosexual intercourse (the reliability of sexual abstinence needs to be evaluated in relation to the duration of the clinical study and the preferred and usual lifestyle of the participant). vii. Vasectomized sexual partner (provided that partner is the sole sexual partner of the WOCBP study participant and that the vasectomized partner has received medical assessment of the surgical success). * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Has distant metastases or radiographically detectable (even if asymptomatic and/or previously treated) central nervous system metastases and/or carcinomatous meningitis as assessed by local site investigator and radiology review. * A WOCBP who has a positive urine pregnancy test within 72 hours prior to first dose of study drug. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. In such cases, the participant must be excluded from participation if the serum pregnancy result is positive. * Participants who received prior radiotherapy treatment or systemic anticancer therapy including any other investigational agents for the HNC under study prior to first dose of study drug. * Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to the first dose of study drug. * History of allergic reactions attributed to compounds of similar chemical or biologic. composition to recombinant proteins, polysorbate 80 or any excipient contained in the drug formulation for CUE-101 or pembrolizumab. * Participants with any history of known or suspected autoimmune disease with the specific exceptions of the following: 1. Vitiligo. 2. Resolved childhood atopic dermatitis. 3. Psoriasis (with exception of psoriatic arthritis) not requiring systemic treatment (within the past 2 years). 4. Participants with a history of Grave's disease that are now euthyroid clinically and by laboratory testing. * History of prior allogeneic bone marrow, stem-cell or solid organ transplantation. * Treatment with corticosteroids (\>10 mg per day prednisone or equivalent) or other immune suppressive drugs within the 7 days prior to the first dose of study drug administration. Steroids for topical, ophthalmic, inhaled, or nasal administration are allowed. Physiological replacement with hydrocortisone up to a maximum dose of 10 mg per day is allowed. * History of clinically significant cardiovascular disease including: 1. Myocardial infarction or unstable angina within the 16 weeks prior to the initiation of study drug. 2. Clinically significant cardiac arrhythmias. 3. Uncontrolled hypertension: systolic blood pressure (BP) \> 180 mmHg, diastolic BP \>100 mmHg. 4. Deep vein thrombosis, pulmonary embolism, stroke, or transient ischemic attack within the 16 weeks prior to the initiation of study drug. 5. QTcB prolongation \> 480 msec. 6. Congestive heart failure (New York heart Association class III-IV). 7. Pericarditis/clinically significant pericardial effusion. 8. Myocarditis. * Clinically significant pulmonary compromise (e.g., requirement for supplemental oxygen) * Clinically significant GI disorders including: 1. History of GI perforation within 1 year prior to study drug administration. Participants with a history of GI perforation that occurred more than 1 year ago can only be enrolled if the sponsor-investigator no longer considers the previously affected area to be at risk for perforation. 2. History of clinically significant GI bleeding within 3 months prior to the initiation of study drug. 3. History of acute pancreatitis within 3 months prior to the initiation of study drug. 4. Diverticulitis that is clinically significant in the opinion of the sponsor-investigator based on the extent or severity of known disease and/or the occurrence of clinically significant disease flares within four weeks prior to the initiation of study drug administration. * Evidence of active viral, bacterial, or systemic fungal infection requiring parenteral treatment within seven days prior to the initiation of study drug. Participants requiring any systemic antiviral, antifungal, or antibacterial therapy for active infection must have completed treatment no less than 1 week prior to the initiation of study drug * Second primary invasive malignancy that has not been in remission for \> 2 years. Exceptions that do not require a 2-year remission include: non-melanoma skin cancer; cervical carcinoma in situ on biopsy; or squamous intraepithelial lesion on Pap smear; localized prostate cancer (Gleason score \<6); or resected melanoma in situ. * History of trauma or major surgery within 4 weeks prior to first dose of study drug. * Has received a live vaccine within 30 days prior to the first dose of study drug. 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, 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. * Has Grade \> 2 audiometric hearing loss. Note: Audiometric abnormalities without corresponding clinical symptoms of Grade \> 2 hearing loss will not be grounds for exclusion. * Has Grade \> 2 neuropathy. * Has Grade \> 2 bleeding due to the underlying malignancy. * Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis. * Active or history of alcohol or other substance abuse within 1 year prior to the initiation of study drug administration. * Participants with uncontrolled intercurrent illness. * Participants with psychiatric illness/social situations that would limit compliance with study requirements, as determined by the treating investigator. * 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. * Any investigative site personnel directly affiliated with this study. * Prisoners or other individuals who are involuntarily detained. * Pregnant women are excluded from this study because it is unknown whether CUE-101 and/or pembrolizumab is an agent with the potential for teratogenic or abortifacient effects. It is unknown whether pembrolizumab is excreted in human milk. Since many drugs are excreted in human milk, and because of the potential for serious adverse reactions in the nursing infant, participants who are breast feeding are not eligible for enrollment.