Valemetostat Tosylate (DS-3201b), an Enhancer of Zeste Homolog (EZH) 1/2 Dual Inhibitor, for Relapsed/Refractory Peripheral T-Cell Lymphoma (VALENTINE-PTCL01)

Inclusion Criteria: * Written informed consent * Participants ≥18 years of age or the minimum legal adult age (whichever is greater) at the time the informed consent form is signed. * Eastern Cooperative Oncology Group performance status of 0, 1, or 2 * Cohort 1 relapsed/refractory peripheral T-cell lymphoma (PTCL): * Diagnosis should be confirmed by the local pathologist; local histological diagnosis will be used for eligibility determination. Participants with the following subtypes of PTCL are eligible according to 2016 WHO classification prior to the initiation of study drug. Any T-cell lymphoid malignancies not listed are excluded. Eligible subtypes include: * Enteropathy-associated T-cell lymphoma * Monomorphic epitheliotropic intestinal T-cell lymphoma * Hepatosplenic T-cell lymphoma * Primary cutaneous γδ T-cell lymphoma * Primary cutaneous CD8+ aggressive epidermotropic cytotoxic T-cell lymphoma * PTCL, not otherwise specified * Angioimmunoblastic T-cell lymphoma * Follicular T-cell lymphoma * Nodal PTCL with T-follicular helper (TFH) phenotype * Anaplastic large cell lymphoma, ALK positive * Anaplastic large cell lymphoma, ALK negative * Cohort 2 relapsed/refractory adult T-cell leukemia/lymphoma (ATL) acute, lymphoma, or unfavorable chronic type. Relapsed/refractory ATL should be confirmed by the local pathologist; local diagnosis will be used for eligibility determination. The positivity of anti-human T-cell leukemia virus type 1 (HTLV-1) antibody will be locally determined for eligibility. * Must have at least one lesion which is measurable in 2 perpendicular dimensions on computed tomography (or magnetic resonance imaging) based on local radiological read * Documented refractory, relapsed, or progressive disease after at least 1 prior line of systemic therapy. * Refractory is defined as: * Failure to achieve CR (or CRu for ATL) after first-line therapy * Failure to reach at least PR after second-line therapy or beyond * Must have at least 1 prior line of systemic therapy for PTCL or ATL. * Participants must be considered hematopoietic cell transplantation (HCT) ineligible during screening due to disease status (active disease), comorbidities, or other factors; the reason for HCT ineligibility must be clearly documented. * In the PTCL cohort, participants with anaplastic large cell lymphoma (ALCL) must have prior brentuximab vedotin treatment. Exclusion Criteria: Participants meeting any exclusion criteria for this study will be excluded from this study. Below is a list of the key exclusion criteria: * Diagnosis of mycosis fungoides, Sézary syndrome and primary cutaneous ALCL, and systemic dissemination of primary cutaneous ALCL * Diagnosis of precursor T-cell leukemia and lymphoma (T-cell acute lymphoblastic leukemia and T-cell lymphoblastic lymphoma), T-cell prolymphocytic leukemia, or T-cell large granular lymphocytic leukemia * Prior malignancy active within the previous 2 years except for locally curable cancer that is currently considered as cured, such as cutaneous basal or squamous cell carcinoma, superficial bladder cancer, or cervical carcinoma in situ, or an incidental histological finding of prostate cancer. * Presence of active central nervous system involvement of lymphoma * History of autologous HCT within 60 days prior to the first dose of study drug * History of allogeneic HCT within 90 days prior to the first dose of study drug * Clinically significant graft-versus-host disease (GVHD) or GVHD requiring systemic immunosuppressive prophylaxis or treatment * Inadequate washout period from prior lymphoma-directed therapy before enrollment, defined as follows: * Prior systemic therapy (eg, chemotherapy, immunomodulatory therapy, or monoclonal antibody therapy) within 3 weeks prior or 5 half-lives of the drug, whichever is longer, to the first dose of study drug * Had curative radiation therapy or major surgery within 4 weeks or palliative radiation therapy within 2 weeks prior to the first dose of study drug * Uncontrolled or significant cardiovascular disease, including: * Evidence of prolongation of QT/QTc interval (eg, repeated episodes of QT corrected for heart rate using Fridericia's method \>450 ms) (average of triplicate determinations) * Diagnosed or suspected long QT syndrome or known family history of long QT syndrome * History of clinically relevant ventricular arrhythmias, such as ventricular tachycardia, ventricular fibrillation, or Torsade de Pointes * Uncontrolled arrhythmia (subjects with asymptomatic, controllable atrial fibrillation may be enrolled) or asymptomatic persistent ventricular tachycardia * Participant has clinically relevant bradycardia of \<50 bpm, unless the participant has a pacemaker * History of second- or third-degree heart block. Candidates with a history of heart block may be eligible if they currently have pacemakers and have no history of fainting or clinically relevant arrhythmia with pacemakers within 6 months prior to Screening * Myocardial infarction within 6 months prior to Screening * Angioplasty or stent craft implantation within 6 months prior to Screening * Uncontrolled angina pectoris within 6 months prior to Screening * New York Heart Association Class 3 or 4 congestive heart failure * Coronary/peripheral artery bypass graft within 6 months prior to Screening * Uncontrolled hypertension (resting systolic blood pressure \>180 mmHg or diastolic blood pressure \>110 mmHg) * Complete left bundle branch block * History of treatment with other EZH inhibitors * Current use of moderate or strong cytochrome P450 (CYP)3A inducers * Systemic treatment with corticosteroids (\>10 mg daily prednisone equivalents). Note: Short-course systemic corticosteroids (eg, prevention/treatment for transfusion reaction) or use for a non-cancer indication (eg, adrenal replacement) is permissible. * Known or suspected hypersensitivity to valemetostat tosylate or any of the excipients