Inclusion Criteria:  Have provided written informed consent Male or female ≥ 18 years of age  Patient has documentation of at least 1 of the following genomic features associated with HRD  Cohort A - any of:  A germline or somatic genetic alteration that is known or suspected to be deleterious in one of the following HR-related genes (ATM, CDK12, PALB2, ARID1A, ATRX, BLM, BARD1, BRIP1, CHEK1, CHEK2, FANCA, FANCF, FANCG, FANCI, FANCL, FANCM, MSH2, NBN, RAD50, RAD51C, RAD51D, WRN) A somatic genetic alteration that is known or suspected to be deleterious in BRCA1 or BRCA2 A prevalent mutational signature 3 as determined by WGS (≥ 20% of total mutations attributed) The presence of a positive HRD status using a NGS assay that includes assessment for genomic instability Cohort A excludes high grade serous ovarian cancer, TNBC, and prostate cancer Cohort B - a pathogenic germline BRCA1 or BRCA2 mutation Note: Genomic features associated with HRD must have been determined from a sample obtained ≤ 12 months before the date of registration into this study with the exception of germline genetic alterations which can have been determined from a sample obtained at any time. Patient agrees to the collection and use of their fresh tumour biopsy sample during screening for WGS Note: A fresh tumour biopsy not required for patients who have had WGS performed within 12 months prior to registration to the study Continues to meet all the inclusion criteria as per the TRIAGE Framework protocol Measurable disease, as defined by RECIST 1.1 (see Appendix 2)  Adequate haematological and end-organ function, defined by the following laboratory results obtained within 7 days prior to registration, independent of blood or platelet transfusion within 2 weeks:  Haemoglobin ≥ 90 g/L ANC ≥ 1.5x109/L Platelet count ≥ 100 x109/L ALT ≤ 3.0 x the ULN, irrespective of the presence or absence of liver metastases AST ≤ 3.0 x the ULN, irrespective of the presence or absence of liver metastases Serum bilirubin ≤ 1.5 x ULN (On fractionation ≤ 90% of total bilirubin should be unconjugated.  Total bilirubin must be <4 x ULN for patients with Gilbert's Syndrome)  Serum creatinine ≤ 1.5x ULN or eGFR ≥ 30 mL/min/1.73 m2 by Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation (appendix 5) INR ≤ 1.5x ULN (≤2.5x ULN if on anticoagulants) Patient has the ability to take oral medications without medical history of malabsorption or other chronic gastrointestinal disease, or other conditions that may harm compliance and/or absorption of the study treatment WOCBP must agree to use a highly effective method of birth control for the duration of the study and for 6 months after the last dose of study treatment (see Appendix 3), and have a negative serum pregnancy test within 7 days of study registration Non-sterile males and their female partners must agree to use a highly effective method of birth control for the duration of the study and for 6 months after the last dose of study treatment. Non- sterile males must avoid sperm donation for the duration of the study and for at least 6 months after the last study drug Female patient must agree not to breastfeed starting at screening and throughout the study period, and for 6 months after the final study drug administration Patient is willing and able to comply with the protocol for the duration of the study including undergoing biopsies, treatment, and scheduled visits and examination including follow up  Exclusion Criteria:  One or more of the exclusion criteria as per the TRIAGE Framework protocol applies  Any previous treatment with a PARP inhibitor  Note: Prior immune checkpoint blockade is permitted provided all the criteria below are met:  Patients must not have received the immune checkpoint blockade within 28 days of study registration Patients must not have experienced a toxicity that led to permanent discontinuation of prior immunotherapy  All AEs while receiving prior immunotherapy must have completely resolved or resolved to grade  1 prior to screening for this study. Patients with an endocrine AE due to immunotherapy are permitted provided they are stably maintained on appropriate replacement therapy and are asymptomatic  Must not have required the use of additional immunosuppression other than corticosteroids for the management of an AE, not have experienced recurrence of an AE if re-challenged, and not require maintenance doses of > 10 mg prednisolone or equivalent per day Any unresolved toxicity (≥CTCAE grade 2) from previous anti-cancer therapy, with the exception of alopecia Note: Patients with irreversible toxicity that is not reasonably expected to be exacerbated by the study treatment (e.g. hearing loss, peripheral neuropathy) are eligible Treatment with strong CYP3A inducers within 10 days (or ≤ 5 half-lives, whichever is shorter) prior to registration. Known need for treatment with strong CYP3A4 inducers during study treatment.  Symptomatic or current history of actively progressing CNS metastases. Patients with a history of treated CNS lesions are eligible, provided that all of the following criteria are met:  Measurable disease per RECIST 1.1 must be present outside the CNS In patients who have received CNS-directed therapy, there is no clinical evidence of interim progression between completion of CNS-directed therapy and registration to the study (radiological re-assessment is not required) The patient has not received radiotherapy within 14 days prior to registration Note: Anticonvulsant therapy at a stable dose is permitted  Note: Patients with asymptomatic brain metastases in which CNS-directed therapy is not indicated are eligible  History of leptomeningeal disease Mean QTc ≥ 470 ms calculated from triplicate ECGs using Fredericia's Correction  Active autoimmune disease or history of autoimmune disease that may relapse, with the following exceptions:  Controlled type 1 diabetes Hypothyroidism managed with no treatment other than with hormone replacement therapy Controlled celiac disease Skin disease not requiring systemic treatment (e.g. vitiligo, psoriasis, alopecia) Any other disease that is not expected to recur in the absence of external triggering factors  Any condition that required systemic treatment with either corticosteroids (> 10 mg daily of prednisone or equivalent) or other immunosuppressive medication within 2 weeks prior to registration, with the following exceptions:  Adrenal replacement steroid (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 or for the treatment of a non- autoimmune condition Positive HIV test at screening Patients with active HBV (chronic or acute; defined as having a positive HBsAg test at screening) or HCV Note: Patients with a past or resolved HBV infection (defined as the presence of HBcAb and absence of HBsAg) are eligible. Patients positive for HCV antibody are eligible only if polymerase chain reaction is negative for HCV RNA Patients with severe chronic or active infections requiring systemic antibacterial, antifungal or antiviral therapy, including active tuberculosis and COVID-19 Patients with a history of interstitial lung disease, non-infectious pneumonitis or uncontrolled systemic diseases, including diabetes, hypertension, pulmonary fibrosis, acute lung diseases, etc. History of non-viral hepatitis or cirrhosis  Any of the following cardiovascular criteria:  Current evidence of cardiac ischemia. Current symptomatic pulmonary embolism. Acute myocardial infarction ≤ 6 months prior to study registration. Heart failure of New York Heart Association Classification III or IV (See Appendix 6) ≤ 6 months prior to study registration. Grade ≥ 2 ventricular arrhythmia ≤ 6 months prior to study registration. History of cerebrovascular accident within 6 months before first dose of study drugs. Has been administered a live vaccine within 4 weeks prior to registration Known sensitivity to any component of pamiparib and/or tislelizumab