• Patient with newly diagnosed, untreated histology-proven PTCL based on local pathology review who is eligible for receiving, Belinostat, Pralatrexate, and CHOP. Pathology material must be available at the site for each patient before enrollment so that it can be sent to the Sponsor (or designee) for later confirmation. The following subtypes, as defined by the updated World Health Organization (WHO) classification, may be included. This information should be available for eligibility:

∙ Pathology subtype:

⁃ Peripheral T-cell lymphoma, not otherwise specified

• Angioimmunoblastic T-cell lymphoma

• Anaplastic lymphoma kinase (ALK)-negative anaplastic large-cell lymphoma (ALCL) patients are eligible only if Brentuximab Vedotin (BV) is not commercially approved for use, not available in the country or patient is contraindicated to receive BV.

• Follicular T-cell lymphoma

• Others: Extra-nodal natural killer/T-cell lymphoma, nasal type; enteropathy-associated T-cell lymphoma; hepatosplenic T-cell lymphoma; and subcutaneous panniculitis-like T-cell lymphoma

‣ CD30 expression and T-cell Follicular Helper (TFH) phenotype status must be available for documentation.

• Patient has at least 1 site of measurable disease according to Response Evaluation Criteria in Lymphoma (RECIL) 2017 criteria as assessed by the local Investigator (Appendix 3)

• Patient has an Eastern Cooperative Oncology Group performance (ECOG) status ≤2

• For Part 1 (Dose Finding) - Patient has adequate hematological, hepatic, and renal function as defined by:

∙ Absolute neutrophil count ≥ 1.5 × 10⁹/L or ≥ 1.0 × 10⁹/L if evidence of bone marrow involvement

‣ Platelet count ≥100×10⁹/L or ≥ 75×10⁹/L if evidence of bone marrow involvement

‣ Total bilirubin ≤1.5 mg/dL

‣ Aspartate aminotransferase (AST)/serum glutamic-oxaloacetic transaminase (SGOT), alanine aminotransferase (ALT)/serum glutamic-pyruvic transaminase (SGPT) ≤ 3×upper limit of normal (ULN; AST/ALT ≤5×ULN if documented hepatic involvement with lymphoma)

‣ Calculated creatinine clearance of ≥ 60 mL/min

• Part 2 (Efficacy and Safety) - disease related hypoplasia, hepatological or renal dysfunction can be included if any of the treatment groups can be administered based on package insert recommendation with the following restrictions:

∙ Absolute neutrophil count ≥ 1.5 × 10⁹/L or ≥ 1.0 × 10⁹/L if evidence of bone marrow involvement

‣ Platelet count ≥100×10⁹/L or ≥ 75×10⁹/L if evidence of bone marrow involvement

‣ Total bilirubin ≤1.5 mg/dL

‣ Aspartate aminotransferase (AST)/serum glutamic-oxaloacetic transaminase (SGOT), alanine aminotransferase (ALT)/serum glutamic-pyruvic transaminase (SGPT) ≤ 3 x the upper limit of normal (ULN; AST/ALT ≤5×ULN if documented hepatic involvement with lymphoma)

‣ Calculated creatinine clearance of ≥ 60 mL/min

• UGT1A1 genotype has been characterized (see Belinostat dose modifications if abnormal) and must be available for documentation.

• Patient must be willing and capable of giving written informed consent and must be able to adhere to dosing and visit schedules and meet all study requirements

• Patient (male or female) is at least 18 years of age at the time of informed consent

• Patient is willing to practice 2 forms of contraception, one of which must be a barrier method, from study entry until at least 6 months after the last dose of study treatment.

⁃ Females of childbearing potential must have a negative urine pregnancy test within 4 weeks prior to the first day of study treatment. Females who are postmenopausal for at least 1 year (defined as more than 12 months since last menses) or are surgically sterilized do not require this test.