Risk-adapted Therapy in HPV-positive Oropharyngeal Cancer Using Circulating Tumor (ct) HPV DNA Profiling (ReACT 2.0)

Inclusion Criteria: * Participants must have histologically or cytologically confirmed, stage I, II, or III, HPV-associated oropharyngeal (tongue base or tonsil) squamous cell carcinoma, as defined by 2017 American Joint Committee on Cancer (AJCC), 8th edition staging. Participants with HPV-associated disease of unknown primary (cT0) are eligible. * Participants who undergo upfront surgery are permitted to enroll if their post-operative pathology necessitates that they receive adjuvant therapy. * Participants who undergo upfront induction chemotherapy with platinum-based therapy are eligible if they have less than a complete clinical or radiologic response to induction as judged by the treating investigator(s). * Participants with locoregionally recurrent disease are eligible if they completed definitive or curative-intent treatment and meet criteria 3.1, 6e below. * HPV status should be confirmed on tissue biopsy or cytologic sample by any of the following: (a) IHC staining for p16 with ≥70% expression, and/or (b) DNA testing (PCR or ISH) for high-risk subtypes 16, 18, 31, 33, or 35. * Tumor tissue available for PD-L1 CPS testing. * Age 18 years or older at the time of informed consent. * Eastern Cooperative Oncology Group (ECOG) performance status ≤1. * Intermediate or high-risk HPV+ disease defined by any one of the following: * TTMV-HPV DNA score \>200 at baseline and failure to clear by \>95% by week 4-5 of treatment * undetectable or low (≤200) TTMV-HPV DNA at baseline prior to treatment with clinical or pathologic T3-4 or N2-3 disease * known HPV subtypes 18, 31, 33, or 35 (but excluding cT1-2N0 participants) * known N3 disease or fixed neck nodes as judged by the treating investigator(s) * any stage disease with known detectable TTMV-HPV DNA 6 weeks or onward from completion of definitive or curative-intent therapy without clinical or radiographic disease and with no additional intervening therapy administered. * Participants should have adequate organ and marrow function to receive adjuvant immunotherapy as outlined below: * Absolute neutrophil count (ANC) ≥1500/µL * Platelets \> 100,000/µL * Hemoglobin ≥9.0g./dL or ≥5.6 mmol/La * Creatinine OR Measured or calculated b creatinine clearance (GFR can also be used in place of creatinine or CrCl) ≤1.5 × ULN OR ≥30 mL/min for participant with creatinine levels \>1.5 × institutional ULN * Total bilirubin ≤1.5 ×ULN OR direct bilirubin ≤ULN for participants with total bilirubin levels \>1.5 × ULN * AST (SGOT) and ALT (SGPT) ≤2.5 × ULN (≤5 × ULN for participants with liver metastases) * International normalized ratio (INR) OR prothrombin time (PT) Activated partial thromboplastin time (aPTT) ≤1.5 × ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants * Ability to understand and the willingness to sign a written informed consent document. * Participants or persons of childbearing potential must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 72 hours prior to the start of therapy. Note: Contraception requirements should conform with CTFG guidelines. The pembrolizumab standard for use of highly effective contraceptive methods for POCBP is 120 days (5 half-lives) after the last dose. Abstaining from breastfeeding after study intervention is at least 5 half-lives or 120 days. Exclusion Criteria: * Participants with AJCC 2017 8th edition stage IV (M1, metastatic) disease. * Pregnant or lactating women. * Has received prior therapy with an anti-PD-1, anti-PD-L1, or another stimulatory or co-inhibitory T-cell receptor treatment. * Uncontrolled intercurrent illness including, but not limited to, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Has received a live vaccine or live-attenuated vaccine within 30 days prior to the first dose of pembrolizumab. * Has a diagnosis of immunodeficiency or is receiving chronic systemic corticosteroid therapy (in doses exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days of first pembrolizumab dosing. * Has active autoimmune disease that has required systemic treatment in past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g. levothyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment and is allowed. Participants with a history of allogeneic tissue/solid organ transplant are excluded. * Has a history of (non-infectious) pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease. * Has an active infection requiring systemic therapy. * Has a known history of uncontrolled human immunodeficiency virus (HIV) infection. No HIV testing is required unless mandated by local health authority. Well-controlled typically includes a CD4+ T-cell count ≥350 cells/mm3 at the time of screening and achieved and maintained virologic suppression defined as confirmed HIV RNA level below 50 or the LLOQ (below the limit of detection) using the locally available assay at the time of screening and for at least 12 weeks before screening. * Has a known history of hepatitis B (defined as hepatitis B surface antigen \[HBsAg\] reactive) or known active hepatitis C virus (defined as HCV RNA \[qualitative\] is detected) infection. Note: no testing for Hepatitis B and Hepatitis C is required unless mandated by local health authority. * Has a known additional malignancy that is progressing or requires active treatment. Exceptions: include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer, and low-risk prostate adenocarcinoma being managed with active surveillance. A history of another separate malignancy in remission without evidence of active disease is permitted if chance of recurrence is thought to be low (in discussion with the Sponsor-investigator). * ALT (SGPT)=alanine aminotransferase (serum glutamic pyruvic transaminase); AST (SGOT)=aspartate aminotransferase (serum glutamic oxaloacetic transaminase); GFR=glomerular filtration rate; ULN=upper limit of normal. a Criteria must be met without erythropoietin dependency and without packed red blood cell (pRBC) transfusion within last 2 weeks. b Creatinine clearance (CrCl) should be calculated per institutional standard.