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), or prior history of acute myeloid leukemia (AML)/myelodysplastic syndrome (MDS). * Has active autoimmune disease that has required systemic treatment in the past year (i.e. with use of steroids or immunosuppressive drugs). Replacement therapy e.g. levothyroxine, insulin, or physiologic corticosteroid doses for adrenal or pituitary insufficiency, etc. are not considered a form of systemic treatment. * Has known history of, or any evidence of active interstitial lung disease, noninfectious pneumonitis, or uncontrolled lung diseases including pulmonary fibrosis, or acute lung diseases. * Has a history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies). * Has known active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA \[qualitative\] is detected). However, if eradicated subject is eligible. * Has received a live vaccine within 28 days of planned start of study therapy. o Note: Vaccines for COVID-19 are allowed except for any live vaccine that may be developed. Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist®) are live attenuated vaccines, and are not allowed within 28 days prior to initiation of treatment. Vaccines should not be given during the chemo-radiation phase until marrow function has normalized as vaccines may not be efficacious during periods of marrow suppression. * Uncontrolled intercurrent illness including but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, uncontrolled cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * Patients receiving any medications or substances that are known to be strong CYP3A inducers (eg. avasimibe, carbamazepine, mitotane, phenobarbital, phenytoin, rifabutin, rifampin/ rifampicin) are ineligible. Patients receiving herbal remedies/medicines such as St. John's Wort (Hypericum perforatum) are also ineligible. See Sections 5.5.2 and 5.5.3 for prohibited medications on study. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated list such as http://medicine.iupui.edu/clinpharm/ddis/table.aspx; medical reference texts such as the Physicians' Desk Reference may also provide this information. As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product. * Pregnant women are excluded from this study because pamiparib is a PARP inhibitor and tislelizumab is a humanized, immunoglobulin G4 (IgG4)-variant monoclonal antibody agent with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with pamiparib and tislelizumab, breastfeeding should be discontinued if the mother is treated with pamiparib and tislelizumab. * HIV-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with pamiparib and tislelizumab. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy. * Disease/procedure significantly affecting gastrointestinal function, such as malabsorption syndrome, resection of the stomach or small bowel, bariatric surgery procedures, symptomatic inflammatory bowel disease, or partial or complete bowel obstruction, or gastrointestinal perforation or fistulae. Note: Gastroesophageal reflux disease under treatment with proton pump inhibitors is allowed (assuming no drug interaction potential).