Induction and Maintenance Treatment With PARP Inhibitor and Immunotherapy in HPV-negative HNSCC

Inclusion Criteria: 1. Patients of both genders, aged ≥18 years; 2. Signed written informed consent; 3. Primary histologically proven p16 negative squamous cell carcinoma of the oral cavity, oropharynx, hypopharynx or larynx amenable to surgery with curative intent. p16 status will be assessed as surrogate marker for HPV infection only for oropharyngeal cancers. p16 status will be assessed using the CINtec p16 Histology assay (Ventana Medical Systems, Tucson, AZ, USA) with strong and diffuse nuclear and cytoplasmic staining in at least 70% of cells used as the cutpoint for positivity. 4. Clinical stage III-IV(M0) according to the VIII edition of AJCC staging system; recurrent/metastatic HNSCC, or previously treated HNSCC with local or systemic therapies, are not eligible for this study. 5. Performance status ECOG 0-1; 6. Availability of fresh tumor tissue via biopsy and provided for study purposes; 7. Willing to provide blood and saliva samples for study purposes; 8. Absence of a second malignancy (except non-melanoma skin cancers, and the following in situ cancers: bladder, gastric, oesophageal, colon, endometrial, cervical/dysplasia, melanoma, or breast) unless a complete remission was achieved at least 2 years prior to study entry AND no additional therapy is required during the study period; 9. Patient has adequate organ and marrow function (absolute neutrophil count ≥ 1500, hemoglobin ≥ 9.0 gram/deciliter (g/dL), platelet count ≥ 100,000, total bilirubin ≤1.5 times institution's upper limit of normal, AST/SGOT and ALT/SPGT ≤ 2.5 times institutional upper limit of normal, albumin ≥ 2.0 g/dL, serum creatinine ≤ 1.5 times institutional upper limit of normal or creatinine clearance ≥ 60 milliliters per minute (mL/min) according to Cockroft-Gault formula, or local institutional standard method); 10. Patient must be able to swallow study drug; 11. Participant must agree to not donate blood during the study or for 90 days after the last dose of study treatment; 12. Female participant has a negative serum pregnancy test within 72 hours prior to taking study treatment if of childbearing potential and agrees to use an adequate method of contraception from screening through 180 days after the last dose of study treatment, or is of nonchildbearing potential. Nonchildbearing potential is defined as follows (by other than medical reasons): * ≥45 years of age and has not had menses for \>1 year * Patients who have been amenorrhoeic for \<2 years without history of a hysterectomy and oophorectomy must have a follicle stimulating hormone value in the postmenopausal range upon screening evaluation * Post-hysterectomy, post-bilateral oophorectomy, or post-tubal ligation. Documented hysterectomy or oophorectomy must be confirmed with medical records of the actual procedure or confirmed by an ultrasound. Tubal ligation must be confirmed with medical records of the actual procedure, otherwise the patient must be willing to use an adequate barrier method throughout the study, starting with the screening visit through 180 days after the last dose of study treatment. See Section 3.3 for a list of acceptable birth control methods. Information must be captured appropriately within the site's source documents. Note: Abstinence is acceptable if this is the established and preferred contraception for the patient. 13. Participant must agree to not breastfeed during the study or for 90 days after the last dose of study treatment; 14. Male participant agrees to use an adequate method of contraception (Section 3.3 for a list of acceptable birth control methods) starting with the first dose of study treatment through 180 days after the last dose of study treatment. Note: Abstinence is acceptable if this is the established and preferred contraception for the patient; 15. Participant must be able to understand the study procedures and agree to participate in the study by providing written informed consent. Exclusion Criteria: 1. Patient has recurrent/metastatic disease; 2. Patient with locally advanced disease not amenable of surgery with curative intent; 3. Patient has received prior local or systemic treatment for HNSCC; 4. Patient with p16/HPV positive HNSCC; 5. Patient with sinonasal, nasal cavity or nasopharyngeal cancer; 6. Patient with SCC on neck disease with unknown primary tumor site; 7. Patient must not be simultaneously enrolled in an interventional clinical trial; 8. Patient must not have had major surgery ≤3 weeks prior to initiating protocol therapy and patient must have recovered from any surgical effects; 9. Participant must not have received investigational therapy ≤ 4 weeks, or within a time interval less than at least 5 half-lives of the investigational agent, whichever is shorter, prior initiating protocol therapy; 10. Participant has had radiation therapy encompassing \>20% of the bone marrow within 2 weeks; or any radiation therapy within 1 week prior to Day 1 of protocol therapy; 11. Participant must not have a known hypersensitivity to niraparib and TSR-042 components or excipients; 12. Participant must not have received a transfusion (platelets or red blood cells) ≤ 4 weeks prior to initiating protocol therapy; 13. Participant must not have received colony stimulating factors (eg, granulocyte colony-stimulating factor, granulocyte macrophage colony stimulating factor, or recombinant erythropoietin) within 4 weeks prior initiating protocol therapy; 14. Participant has had any known Grade 3 or 4 anemia, neutropenia or thrombocytopenia due to prior chemotherapy that persisted \> 4 weeks and was related to the most recent treatment; 15. Participant must not have any known history of myelodysplastic syndrome (MDS) or acute myeloid leukemia (AML); 16. Participant must not have a serious, uncontrolled medical disorder, non-malignant systemic disease, or active, uncontrolled infection. Examples include, but are not limited to, uncontrolled ventricular arrhythmia, recent (within 90 days) myocardial infarction, uncontrolled major seizure disorder, unstable spinal cord compression, superior vena cava syndrome, or any psychiatric disorder that prohibits obtaining informed consent; 17. Participant must not have known, symptomatic brain or leptomeningeal metastases; 18. Patient experienced ≥ Grade 3 immune-related adverse event with prior immunotherapy, with the exception of non-clinically significant lab abnormalities; 19. Participant has a diagnosis of immunodeficiency or has received systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to initiating protocol therapy; 20. Any concurrent chemotherapy, Investigational Product, biologic, or hormonal therapy for cancer treatment; 21. Subjects with previous malignancies (except non-melanoma skin cancers, and the following in situ cancers: bladder, gastric, oesophageal, colon, endometrial, cervical/dysplasia, melanoma, or breast) unless a complete remission was achieved at least 2 years prior to study entry AND no additional therapy is required during the study period; 22. Subjects with an active, known or suspected autoimmune disease. Subjects with type I diabetes mellitus, hypothyroidism only requiring hormone replacement, skin disorders (such as vitiligo, psoriasis, or alopecia) not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll; 23. Subjects with a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalent) or other immunosuppressive medications within 14 days of enrollment. Inhaled or topical steroids, and adrenal replacement steroid \> 10 mg daily prednisone equivalent, are permitted in the absence of active autoimmune disease; 24. Subjects with interstitial lung disease that is symptomatic or may interfere with the detection or management of suspected drug-related pulmonary toxicity; 25. Known psychiatric or substance abuse disorder that would interfere with cooperation with the requirements of the trial; 26. Known active Hepatitis B infection (defined as presence of HBsAg and/or HBV DNA), active hepatitis C infection (defined as presence of Hep C RNA) and/or known Human Immunodeficiency Virus (HIV). Patients with HIV who have a normal CD4 count (≥ 200) and an undetectable viral load are not excluded; 27. Pregnant or breast-feeding patients. Women of childbearing potential must have a negative pregnancy test performed within 72 hours before treatment start. Both men and women enrolled in this trial must use adequate barrier birth control measures during the course of the trial and 180 days after the last dose of study treatment; 28. Known medical condition that, in the investigator's opinion, would increase the risk associated with study participation or study drug administration or interfere with the interpretation of safety results; 29. History or current evidence of any condition that, in the opinion of the treating investigator, might interfere with the subject's participation for the full duration of the trial. 30. Participant has received a live vaccine within 14 days of initiating protocol therapy.