Inclusion Criteria:

          -  Biopsy proven, histological confirmed renal cell carcinoma (RCC) or renal medullary
             carcinoma (RMC).. Patients with surgery and biopsy at outside institutions will be
             eligible for this protocol once archival material is reviewed and the above diagnosis
             confirmed by genitourinary pathology review at Memorial Sloan Kettering Cancer Center
             (MSKCC).

        Cohort 1:

          -  Presence of VHLalteration by next-generation sequencing (NGS) with a stateapproved
             assay

          -  Patients must have radiographic evidence of disease progression after treatment with
             at least one prior PD-1 or PD-L1 agent, and one prior VEGF inhibitor

          -  Maximum 3 prior lines of therapy

        Cohort 2:

          -  For FH/SDH patients FH- or SDH- expression-loss by immunohistochemistry (IHC) or
             alteration (somatic or germline) in FH or SDH per NGS with a state-approved assay

          -  For Renal Medullary Carcinoma (RMC) patients: histologic confirmation of RMC (no
             IHC/NGS criteria required)

          -  At least one prior line of therapy:

          -  For FH/SDH patients Patients must have radiographic evidence of disease progression
             after treatment with at least one prior line of therapy (one prior PD-1/PD-L1 and/or
             VEGF inhibitor).

          -  For Renal Medullary Carcinoma (RMC) patients prior radiographic evidence of disease
             progression on/after at least one line of chemotherapy (e.g. carboplatin / paclitaxel,
             carboplatin / paclitaxel / bevacizumab, carboplatin / gemcitabine, and gemcitabine /
             doxorubicin).

          -  No maximum lines of therapy

        Both Cohorts 1 & 2

          -  Adequate Hematologic Function

          -  Absolute Neutrophil Count ≥ 1.5 x 10^9 / L

          -  Platelet Count ≥ 100 x 10^9 / L

          -  Hemoglobin ≥ 9 g/dL

          -  No transfusion of packed red blood cells or platelets within 21 days of Cycle 1 Day 1

          -  Adequate Renal Function ≥ 30 ml/min according to the Cockcroft-Gault Equation

          -  Patients with moderate renal impairment (creatinine clearance 30-59 by Cockcroft-Gault
             EquationI) will start with a reduced dose of talazoparib.

          -  Adequate Hepatic Function including:

          -  Total bilirubin ≤ 1.5 x upper limit of normal (ULN)

          -  AST ≤ 3 x upper limit of normal (ULN) without liver metastasis

          -  ALT ≤ 3 x upper limit of normal (ULN) without liver metastasis

          -  AST or ALT ≤ 5 x upper limit of normal (ULN) for patients with liver metastasis

          -  Patients with known Gilbert's syndrome may be included if total bilirubin ≤ x 3 ULN

          -  Eastern Cooperative Group (ECOG) Performance Status 0-2.

          -  Patients must have measurable disease by RECIST v1.1. At least one measurable lesion
             should not have been previously irradiated.

          -  Women of childbearing potential must have negative serum pregnancy testing at
             screening. All women will be considered childbearing potential unless meeting criteria
             including:

          -  Achieved post-menopausal status as defined by cessation of regular menses for at least
             12 consecutive months with no alternative pathological or physiological cause and have
             follicular stimulation hormone showing postmenopausal state. Women who have been
             amenorrhoeic for ≥12 months are still considered to be of childbearing potential if
             the amenorrhea is possibly due to prior chemotherapy, anorexia, low body weight,
             ovarian suppression, anti-estrogen therapy or other medically inducible reasons.

          -  Documented hysterectomy or bilateral oophorectomy surgery

          -  Medically confirmed ovarian failure

          -  Sexually active participants and their partners must agree to use medically accepted
             methods of contraception (i.e. barrier methods including condoms, female condom, or
             diaphragm with spermicidal gel) during the study and for 7 months after the last dose
             of the study treatment for females, and 4 months for males.

          -  Recovery of baseline CTCAE v5.0 grade ≤1 toxicities related to prior study treatments
             unless adverse events are clinically non-significant and/or stable on supportive
             therapy if needed.

          -  Patients must be willing and able to comply with trial protocol. This includes
             adhering to the treatment plan, scheduled visits, laboratory and other study
             procedures.

        Exclusion Criteria:

          -  Patients < 18 years old

          -  Patients who are pregnant or breast-feeding. Fertile patients who are unwilling or
             unable to use two methods of contraception (at least one of which considered highly
             effective) for duration of study and after 7 months after last dose of study treatment
             for female, and 4 months for males.

          -  Patients who had prior immune checkpoint blockade therapy (either anti-PD-1, anti-
             PD-L1 and/or anti-CTLA-4) discontinued due to development of an immune related adverse
             event.

          -  Prior diagnosis of myelodysplastic syndrome (MDS) or diagnosis of other malignancy
             that requires anti-cancer directed therapy within the last 24 months. Exclusions
             include those cancers that are considered cured by local therapy (i.e.Basal cell
             carcinoma, squamous cell carcinoma, ducal carcinoma in situ of breast, bladder of
             cervix) or other cancers that have low malignant potential and do not require systemic
             therapy (i.e. Gleason-grade <6 prostate adenocarcinoma, borderline ovarian malignancy
             / low malignant potential).

          -  Prior treatment with talazoparib or other agents that target PARP

          -  Treatment with anti-cancer therapies within 21 days or five half-lives, whichever
             shorter, of start date, including monoclonal antibody, cytotoxic therapy, or another
             investigational agent. There is no specific time window between last PD-1/PD-L1
             therapy and start date of new therapy on protocol.

          -  Significant vascular disease (i.e. aortic aneurysm requiring surgical repair, recent
             arterial thrombosis) within 6 months prior to first dose of therapy.

          -  Evidence of bleeding diathesis or significant unexplained coagulopathy (i.e. absent of
             anticoagulation)

          -  Clinical signs or symptoms of gastrointestinal obstruction requirement parenteral
             hydration, parenteral nutrition, or feeding tube.

          -  Uncontrolled effusion management (pleural effusion, pericardial effusion, or ascites)
             which requires recurrent drainage procedures.

          -  Patients treated with systemic immunosuppressants; except for

               1. chronic physiologic replacement of ≤ 10mg prednisone (or equivalent) for
                  treatment of adrenal insufficiency; Steroids required for pre-medication
                  reactions

               2. Local steroid use is permitted (e.g. intranasal, topical, inhaled, or local
                  steroid injection, i.e. intra-articular)

          -  Patients with autoimmune disease that may worsen during immune checkpoint blockade
             therapy are excluded. Patients with diabetes type I, vitiligo, psoriasis, hypo- or
             hyperthyroid disease not requirement immunosuppressive treatment as above are
             eligible.

          -  Prior organ transplantation including allogeneic stem cell transplant.

          -  No active infection requiring parenteral antibiotic therapy.

          -  Prior diagnosis of HIV/AIDS

          -  History of either positive HCV RNA viral load or anti-HCV antibody screening
             detectable; HBV infection with HBV surface antigen detection and/or positive HBV DNA
             viral load.

          -  Known hypersensitivity to talazoparib or avelumab, or any component in formulations.
             Patients with known hypersensitivity to monoclonal antibodies (Grade ≥3 by CTCAE v5.0)

          -  Live vaccination within 4 weeks of first dose of therapy. All vaccines except
             inactivated are prohibited while on study.

          -  Severe acute or chronic medical conditions which may significantly increase the risk
             of study participants, per treating investigator's discretion

          -  Radiation therapy to any site (including bone) <2 weeks prior to the first dose of
             therapy. Patients with clinically relevant ongoing complications from prior radiation
             therapy, per investigators' assessment, are not eligible.

          -  Symptomatic brain metastasis or leptomeningeal disease requiring steroid use. Patients
             are eligible if they neurologically stable for 4 weeks, and have completed radiation
             therapy or surgery, and recovered from side effects. Patients must have discontinued
             steroid therapy for at least 2 weeks prior to first dose of study treatment.

          -  Current or anticipated use of potent P-gp inhibitors within 7 days prior to
             randomization or anticipated use during the study. Please see Appendix 5 for a list of
             potent P-gp inhibitors.

          -  Inability to swallow capsules, known intolerance to talazoparib or its excipients,
             known malabsorption syndrome, or other conditions which impair intestinal absorption.

          -  Investigator site staff members directly involved in study conduct, including but not
             limited to their family members, or patients who are Pfizer members, including their
             family members, who are directly involved in study conduct.