Inclusion Criteria:

1. Prior SOT of kidney, liver, heart, lung, pancreas, small bowel, or any combination of these (SOT cohort); or prior allogeneic HCT (HCT cohort)
2. A diagnosis of locally-assessed, biopsy-proven EBV+ PTLD
3. Availability of appropriate partially HLA-matched and restricted tabelecleucel has been confirmed by the sponsor
4. Measurable, 18F-deoxyglucose (FDG)-avid (Deauville score ≥ 3) systemic disease using Lugano Classification response criteria by positron emission tomography (PET)-diagnostic computed tomography (CT), except when contraindicated or mandated by local practice, then magnetic resonance imaging (MRI) may be used.For subjects with treated central nervous system (CNS) disease, a head CT and/or brain/spinal MRI as clinically appropriate will be required to follow CNS disease response per Lugano Classification response criteria.
5. Treatment failure of rituximab or interchangeable commercially available biosimilar monotherapy (SOT subgroup A or HCT cohort) or rituximab plus any concurrent or sequentially administered chemotherapy regimen (SOT subgroup B) for treatment of PTLD.
6. Eastern Cooperative Oncology Group performance status ≤ 3 for subjects aged ≥ 16 years; Lansky score ≥ 20 for subjects < 16 years
7. For HCT cohort only: If allogeneic HCT was performed as treatment for an acute lymphoid or myeloid malignancy, the underlying primary disease for which the subject underwent transplant must be in morphologic remission
8. Adequate organ function

1. Absolute neutrophil count ≥ 1000/μL, (SOT cohort) or ≥ 500/μL (HCT cohort), with or without cytokine support
2. Platelet count ≥ 50,000/μL, with or without transfusion or cytokine support. For HCT cohort, platelet count < 50,000/μL but ≥ 20,000/μL, with or without transfusion support, is permissible if the subject has not had grade ≥ 2 bleeding in the prior 4 weeks (where grading of the bleeding is determined per the National Cancer Institute's Common Terminology Criteria for Adverse Events \[CTCAE\], version 5.0)
3. Alanine aminotransferase (ALT), aspartate aminotransferase (AST), and total bilirubin each < 5 × the upper limit of normal; however, ALT, AST, and total bilirubin each ≤ 10 × upper limit of normal is acceptable if the elevation is considered by the investigator to be due to EBV and/or PTLD involvement of the liver as long as there is no known evidence of significant liver dysfunction
9. Subject or subject's representative is willing and able to provide written informed consent

Exclusion Criteria:

1. Burkitt lymphoma, classical Hodgkin lymphoma, or any T cell lymphoma
2. Daily steroids of > 0.5 mg/kg prednisone or glucocorticoid equivalent, ongoing methotrexate, or extracorporeal photopheresis
3. Untreated CNS PTLD or CNS PTLD for which the subject is actively receiving CNS-directed chemotherapy (systemic or intrathecal) or radiotherapy at enrollment. NOTE:Subjects with previously treated CNS PTLD may enroll if CNS-directed therapy is complete.
4. Suspected or confirmed grade ≥ 2 graft-versus-host disease (GvHD) per the Center for International Blood and Marrow Transplant Research consensus grading system at enrollment
5. Ongoing or recent use of a checkpoint inhibitor agent (eg, ipilimumab, pembrolizumab, nivolumab) within 3 drug half-lives from the most recent dose to enrollment
6. For HCT cohort: active adenovirus viremia
7. Need for vasopressor or ventilatory support
8. Antithymocyte globulin or similar anti-T cell antibody therapy ≤ 4 weeks prior to enrollment
9. Treatment with Epstein-Barr virus cytotoxic T lymphocytes or chimeric antigen receptor T cells directed against B cells within 8 weeks of enrollment (SOT or HCT cohorts), or unselected donor lymphocyte infusion within 8 weeks of enrollment (HCT cohort only)
10. Female who is breastfeeding or pregnant or female of childbearing potential or male with a female partner of childbearing potential unwilling to use a highly effective method of contraception
11. Inability to comply with study-related procedures