Inclusion Criteria:  At least 18 years of age on the day of signing informed consent Histologically or cytologically confirmed new diagnosis of squamous cell carcinoma of the larynx (glottic or supraglottic). Stages III, IVA, or IVB according to the AJCC (American Joint Cancer Committee) staging manual, 8th edition  Male participants:  A male participant must agree to use a contraception as detailed in Appendix 3 of this protocol 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.  Female participants:  A female participant is eligible to participate if she is not pregnant (see Appendix 3), not breastfeeding, and at least one of the following conditions applies:  Not a woman of childbearing potential (WOCBP) OR 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. The participant (or legally acceptable representative if applicable) provides written informed consent for the trial. If available, provision of an archived tumor tissue block (or at least 20 newly cut unstained slides) where such samples exist in a quantity sufficient to allow for analysis. A recent (≤3 months) tumor biopsy prior to treatment initiation is an optional requirement, provided that a biopsy procedure is technically feasible, and the procedure is not associated with unacceptable clinical risk. For patients without an available archival sample and who decline a new biopsy prior to study entry, enrolment without tissue provision will be allowed. Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1 Have adequate organ function  Exclusion Criteria:  Large volume T4 disease, defined as invasion through the cartilage or extension > 1 cm to the base of the tongue T1 disease, defined as tumor limited to one subsite of the supraglottis or limited to the vocal cords, with normal vocal-cord mobility, according to the TNM staging system. Contra indication, in the opinion of the treating physician, for radiotherapy, carboplatin or paclitaxel.  A WOCBP who has a positive urine pregnancy test within 72 hours prior to treatment initiation. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. 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. Note: This table includes eligibility-defining laboratory value requirements for treatment; laboratory value requirements should be adapted according to local regulations and guidelines for the administration of specific chemotherapies.  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, OX-40, CD137). Has received any prior systemic anti-cancer therapy for management of the participant's current cancer, including investigational agents prior to allocation. Has received prior radiotherapy to the neck  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 (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.  Is currently participating in or has participated in a study of an investigational agent with anti-cancer activity or has used an investigational device within 4 weeks prior to the first dose of study intervention. 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.  Has a history of a second malignancy, unless potentially curative treatment has been completed with no evidence of malignancy for 2 years.  Note: The time requirement does not apply to participants who underwent successful definitive resection of basal cell carcinoma of the skin, squamous cell carcinoma of the skin, superficial bladder cancer, in situ cervical cancer, or other in-situ cancers  Has severe hypersensitivity (≥Grade 3) to pembrolizumab, carboplatin, paclitaxel and/or any of their excipients. Has 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, etc.) is not considered 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. Has a known history of Human Immunodeficiency Virus (HIV) infection. Note: No HIV testing is required  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 detected) infection.  Note: no testing for Hepatitis B and Hepatitis C is required  Has known active TB (Bacillus Tuberculosis). Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the subject to participate, in the opinion of the treating investigator. Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. 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 trial treatment. Has had an allogenic tissue/solid organ transplant.