Dosing Study of Radiation Combined With Tislelizumab and Pamiparib in Patients With Previously Treated Head and Neck Cancer

Inclusion Criteria: * Clinically documented recurrent head and neck cancer requiring regional therapy. * Human papillomavirus (HPV) testing for oropharynx primary tumors by p16 immunohistochemistry (IHC) positivity * Availability of more than (or equal to) 10 unstained 5 micron slides (to be provided to Human Tissue Resource Center at the University of Chicago). Subjects who cannot fulfill this requirement will need to undergo a new biopsy prior to enrollment on study. * Recurrent or second primary, previously irradiated head and neck squamous cell carcinoma without clinically measurably distant metastatic disease, or low volume oligometastatic disease amenable to Stereotactic Body Radiation Therapy (SBRT) or other curative-intent therapy (e.g. surgery, radiation frequency ablation therapy) * Prior radiation therapy completed in 4 months (or longer) , and/or chemotherapy, immunotherapy, or targeted therapy completed 1 month (or earlier) before study entry, and patient should have recovered from any adverse effects. * Prior programmed death-1 (PD-1)/ programmed death ligand-1 (PD-L1) inhibition is permitted. * Prior chemotherapy is permitted. * Patients who undergo surgical salvage therapy with positive margin or extranodal extension or other high-risk patients determined during multidisciplinary tumor board who are eligible for adjuvant re-irradiation therapy are eligible. * 18 years of age and older. * Eastern Cooperative Oncology Group performance status of one or less. * Life expectancy of greater than 12 weeks. * Negative serum or urine pregnancy test at screening for patients of childbearing potential. * Patients must have normal organ and marrow functions as defined by lab values that will be confirmed by the study doctor. * Age, Sex, and Reproductive Status: 1. Women of childbearing potential (WOCBP=premenopausal woman capable of becoming pregnant) must have a negative serum or urine pregnancy test within 24 hours prior to the start of study drug. 2. Women must not be breastfeeding. 3. WOCBP must agree to follow instructions for highly effective method(s) of contraception for the duration of treatment and for 180 days (6 months) after the last dose of study drug(s). 4. Men who are sexually active with WOCBP must agree to follow instructions for method(s) of contraception for the duration of treatment with study drug(s) plus 180 days (6 months) after the last dose of study drug(s). 5. Azoospermic males and WOCBP who are continuously not heterosexually active are exempt from contraceptive requirements. Females must still undergo pregnancy testing as described in this section. Investigators shall counsel WOCBP and male subjects who are sexually active with WOCBP on the importance of pregnancy prevention and the implications of an unexpected pregnancy. Investigators shall advise WOCBP and male subjects who are sexually active with WOCBP on the use of highly effective methods of contraception. Highly effective methods of contraception have a failure rate of \<1% when used consistently and correctly. * At a minimum subjects must agree to the use of one method of highly effective contraception as listed in Appendix D. In addition, male subjects are expected to use a condom as noted in Appendix D. The effects of tislelizumab and pamiparib on the developing human fetus are unknown. For this reason and because monoclonal antibodies and PARP inhibitor agents are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 6 months after completion of pamiparib and tislelizumab administration. * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * • Previously untreated patients with locoregional-only disease are not eligible. * Patients who have had chemotherapy within 4 weeks prior to entering the study, or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier. * Patients may not be receiving any other investigational agents. * History of allergic reactions attributed to compounds of similar chemical composition or excipients used in the study. * Any condition that required systemic treatment with either corticosteroids (\> 10 mg daily of prednisone or equivalent) or other immunosuppressive medication ≤ 14 days before the first dose of study drug(s). * Note: Patients who are currently or have recently been on any of the following corticosteroid regimens are not excluded: * Adrenal replacement corticosteroid (dose ≤ 10 mg daily of prednisone or equivalent) * Topical, ocular, intra-articular, intranasal, or inhalational corticosteroid with minimal systemic absorption * Short course (≤ 7 days) of corticosteroid prescribed prophylactically (e.g., for contrast dye allergy) or for the treatment of a nonautoimmune condition (e.g., delayed-type hypersensitivity reaction caused by contact allergen) * Has hypersensitivity to tislelizumab, pamiparib, or any other drug used in this protocol. * Has a known history of active tuberculosis (Bacillus Tuberculosis infection) * 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 or any tumors that are not likely to influence live expectancy in the subsequent 3 years without active treatment (e.g. low grade prostate cancer in absence of therapy),