• Male/female participants who are at least 21 years of age on the day of signing informed consent with histologically or cytologically-confirmed diagnosis of peripheral T-cell lymphoma (PTCL), including angioimmunoblastic T-cell lymphoma (AITL), peripheral T-cell lymphoma of T-follicular helper cell derivation (PTCL-TFH), anaplastic large cell lymphoma (ALCL), NK/T-cell lymphoma (NKTCL), gamma-delta T cell lymphoma (GDTL), enteropathy associated T-cell lymphoma (EATL), monomorphic epitheliotropic intestinal T-cell lymphoma (MEITL), subcutaneous panniculitis like T-cell lymphoma, and PTCL, not otherwise specified (PTCL-NOS) will be enrolled in this study.

• Male participants:

• A male participant must agree to use a contraception as detailed in Appendix 3 of this protocol during the treatment period and for at least the time needed to eliminate the study intervention (180 days for Olaparib; no requirement for pembrolizumab) after the last dose of study treatment and refrain from donating sperm during this period.

• A female participant is eligible to participate if she is not pregnant (see Appendix 3), not breastfeeding, and at least one of the following conditions applies: a. Not a woman of childbearing potential (WOCBP) as defined in Appendix 3 OR b. A WOCBP who agrees to follow the contraceptive guidance in Appendix 3 during the treatment period and for at least the time needed to eliminate the study intervention (180 days for Olaparib; 120 days for pembrolizumab) after the last dose of study treatment.

• Participants must have progressed on treatment with at least one prior systemic anti-cancer therapy including investigational agents. These may include an anti-PD-1/L1 mAb administered either as monotherapy or in combination with other checkpoint inhibitors or other therapies. PD-1 treatment progression is defined by meeting all of the following criteria:

∙ Has received at least 2 doses of an approved anti-PD-1/L1 mAb.

‣ Has demonstrated disease progression after anti-PD-1/L1 as defined by Cheson response criteria. The initial evidence of PD is to be confirmed by a second assessment no less than 4 weeks from the date of the first documented disease progression, in the absence of rapid clinical progression (as defined in 4.c).

‣ Progressive disease has been documented within 12 weeks from the last dose of anti-PD-1/L1 mAb.

⁃ Progressive disease is determined according to Cheson response criteria.

• This determination is made by the investigator. Once disease progression is confirmed, the initial date of disease progression documentation will be considered the date of disease progression.

• Progression on other systemic anti-cancer therapy including investigational agents is defined by radiographic disease progression based on Cheson response criteria.

• The participant (or legally acceptable representative if applicable) provides written informed consent for the trial.

• Have measurable disease based on Cheson criteria. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions.

• Archival tumor tissue sample or newly obtained \[core, incisional or excisional\] biopsy of a tumor lesion not previously irradiated has been provided. Formalin-fixed, paraffin embedded (FFPE) tissue blocks are preferred to slides. Newly obtained biopsies are preferred to archived tissue.

• Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1. Evaluation of ECOG is to be performed within 7 days prior to the first dose of study intervention.

• Have adequate organ function as defined in the following. Specimens must be collected within 10 days prior to the start of study intervention.

‣ Absolute neutrophil count (ANC)≥500/μL

⁃ Platelets ≥25 000/μL

⁃ Hemoglobin ≥8 g/dL

⁃ Creatinine OR Measured or calculated creatinine clearance (GFR can also be used in place of creatinine or CrCl) ≤1.5 × ULN OR ≥30 mL/min for participant with creatinine levels \>1.5 × institutional ULN

⁃ Total bilirubin ≤1.5 ×ULN OR direct bilirubin ≤ULN for participants with total bilirubin levels \>1.5 × ULN

⁃ AST (SGOT) and ALT (SGPT) ≤2.5 × ULN (≤5 × ULN for participants with liver metastases)

⁃ International normalized ratio (INR) OR prothrombin time (PT) ≤1.5 × ULN unless participant is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants

⁃ Activated partial thromboplastin time (aPTT) ≤1.5 × ULN unless participant is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants

⁃ Hepatitis B and C screening tests are required:

∙ Hepatitis B positive subjects

⁃ Participants who are HBsAg positive are eligible if they have received HBV antiviral therapy for at least 4 weeks and have undetectable HBV viral load prior to enrolment.

• Participants should remain on anti-viral therapy throughout study intervention and follow local guidelines for HBV anti-viral therapy post completion of study intervention.

‣ Participants with history of HCV infection are eligible if HCV viral load is undetectable at screening.

⁃ Participants must have completed curative anti-viral therapy at least 4 weeks prior to enrolment.

⁃ Participant has a life expectancy of at least 3 months