Inclusion Criteria:  Histological diagnosis of squamous cell carcinoma of the oral cavity, oropharynx, hypopharynx or larynx  Intermediate or high-risk disease defined by the following:  Squamous Cell Carcinoma of the oral cavity, larynx or hypopharynx American Joint Committee on Cancer (AJCC) 8th Stage III-IVB p16-Negative oropharynx SCC, AJCC 8th Stage III-IVB p16--positive oropharyngeal SCC, AJCC 8th stage II-III Tumor must have documented Programmed Death (PD) Ligand (L) -1 Combined Positive Score (CPS) PD-L1 CPS ≥ 1 by immunohistochemistry (IHC). Prior therapy for advanced stage HNSCC with definitive Standard of Care (SoC) CRT Intensity Modulated Radiation Therapy (IMRT (66-70 Gy) with concurrent Cisplatin with curative intent. Patients must have received a total cumulative dose of cisplatin of ≥ 200 mg/m2 or equivalent carboplatin plus taxanes combination per investigator criteria during concurrent treatment. No clinical or radiographic evidence of progressive disease at the time of enrollment. Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) ≤ 2.  Adequate bone marrow function, including:  Absolute Neutrophil Count (ANC) ≥ 1,000/µL or ≥ 1.0 x 10^9/L. Platelets ≥ 75,000/µL or ≥ 100 x 10^9/L. Hemoglobin ≥ 8 g/dL (may have been transfused). Adequate renal function, as determined by an estimated creatinine clearance ≥ 30 mL/min as calculated using the Cockcroft- Gault.  Adequate liver function, including:  Total serum bilirubin ≤ 1.5 x upper limit of normal (ULN) Aspartate and alanine aminotransferase (AST and ALT) < 2.5 x ULN. Pregnancy test (for patients of childbearing potential) negative at screening. Male patients able to father children and female patients of childbearing potential and at risk for pregnancy must agree to use two methods of contraception (at least one of which is considered to be highly effective throughout the study and for at least 3 months after the last dose of cemiplimab-rwlc. Evidence of a signed and dated informed consent document indicating that the patient (or a legally acceptable representative, as allowed by local guideline/practice) has been informed of all pertinent aspects of the study.  Exclusion Criteria:  Prior immunotherapy with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, or anti-Cytotoxic T lymphocyte Associated (CTLA)-4 antibody (including ipilimumab), or any other antibody or drug specifically targeting T cell co-stimulation or immune checkpoint pathways. Major surgery ≤ 4 weeks prior to enrollment. Prior malignancy (other than the current Head and Neck cancer or in situ disease) requiring tumor-directed therapy within the last 2 years prior to enrollment, or concurrent malignancy associated with clinical instability. Exceptions for disease within the 2 years are superficial esophageal cancer (TIS or T1a) fully resected by endoscopy, prostate cancer (Gleason score ≤6) either curatively treated or deemed to not require treatment, ductal in situ carcinoma of the breast that has completed curative treatment, adequately treated basal cell or squamous cell skin cancer. Active autoimmune disease that might deteriorate when receiving an immunostimulatory agent. Patients with diabetes type I, vitiligo, psoriasis, or hypo- or hyperthyroid disease not requiring immunosuppressive treatment are eligible. Active infection requiring systemic therapy.  Use of immunosuppressive medication at time of enrollment, except the following:  Intranasal, inhaled, topical steroids, or local steroid injections (eg, intra-articular injection); b. Systemic corticosteroids at physiologic doses ≤10 mg/day of prednisone or equivalent Steroids as premedication for hypersensitivity reactions (eg, CT scan premedication). Prior organ transplantation including allogenic stem-cell transplantation. Diagnosis of prior immunodeficiency or known human immunodeficiency virus (HIV) or acquired immunodeficiency syndrome (AIDS) related illness. Hepatitis B virus (HBV) or hepatitis C virus (HCV) infection at screening (positive HBV surface antigen or HCV RNA [ribonucleic acid] if anti-HCV antibody screening test positive). Pregnant female patients, breastfeeding female patients, and male patients able to father children and female patients of childbearing potential who are unwilling or unable to use 2 methods of contraception (at least one of which is considered to be highly effective) for at least 3 months after the last dose of cemiplimab-rwlc. Patients with impaired decision-making capacity.