Study of Pembrolizumab (MK-3475) in Combination With Romidepsin

Inclusion Criteria: 1. Patients with peripheral T-cell lymphoma (including but not limited to PTCL-NOS, angioimmunoblastic T-cell lymphoma, anaplastic large T-cell lymphoma). Patients with mycosis fungoides with large cell transformation with measurable disease are eligible. 2. Disease status defined as refractory to or relapsed after ≥ 1 prior treatment lines. 3. Patients irrespective of transplant eligibility status can be enrolled; however patients can be seen by SCT team in anticipation for SCT. 4. Subjects with ALK+ ALCL should have been treated with, be ineligible for, or have refused chemotherapy and brentuximab prior to enrollment on the current study. 5. Patients with a measurable disease, defined by a node or mass with the longest diameter ≥ 1.5cm. Inclusion Criteria: In order to be eligible for participation in this trial, the subject must: 1. Be willing and able to provide written informed consent/assent for the trial. 2. Be 18 years of age on day of signing informed consent. 3. Patients with PTCL should have radiographically measurable disease \>/= 1.5cm. 4. Be willing to provide tissue from a newly obtained core or excisional biopsy of a tumor lesion. Newly-obtained is defined as a specimen obtained up to 12 weeks(84 days) prior to initiation of treatment on Day 1. Subjects for whom newly-obtained samples cannot be provided (e.g. inaccessible or subject safety concern) may submit an archived specimen. 5. Have a performance status of 0, 1 or 2 on the ECOG Performance Scale. 6. Demonstrate adequate organ function as defined in Table 1, all screening labs should be performed within 14 days of treatment initiation. Table 1 Adequate Organ Function Laboratory Values System Laboratory Value * Hematological * Absolute neutrophil count (ANC) ≥ 1000 /mcL * Platelets ≥100,000 / mcL. If bone marrow is involved, platelets should be at least 50K and ANC 750 / mcL * Hemoglobin ≥ 8g/dL without transfusion or EPO dependency (within 7 days of assessment) * Renal * Serum creatinine OR Measured or calculateda creatinine clearance (GFR can also be used in place of creatinine or CrCl) ≤1.5 X upper limit of normal (ULN) OR ≥60 mL/min for subject with creatinine levels \> 1.5 X institutional ULN * Hepatic * Serum total bilirubin ≤ 1.5 X ULN OR Direct bilirubin ≤ ULN for subjects with total bilirubin levels \> 1.5 ULN * AST (SGOT) and ALT (SGPT) ≤ 2.5 X ULN OR ≤ 5 X ULN for subjects with liver metastases * Albumin \> 2 mg/dL * Coagulation International Normalized Ratio (INR) or Prothrombin Time (PT) Activated Partial Thromboplastin Time (aPTT) ≤1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants ≤1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants aCreatinine clearance should be calculated per institutional standard. 7. Female subject of childbearing potential should have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. 8. Female subjects of childbearing potential (Section 5.7.2) must be willing to use an adequate method of contraception as outlined in Section 5.7.2 - Contraception, for the course of the study through 120 days after the last dose of study medication. Note: Abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject. 9. Male subjects of childbearing potential (Section 5.7. .2 must agree to use an adequate method of contraception as outlined in Section 5.7. .2- Contraception, starting with the first dose of study therapy through 120 days after the last dose of study therapy. Note: Abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject. 10. Relapsed/refractory Cutaneous T cell Lymphomas (CTCL) patients with transformed and aggressive T Cell with predominant lymph node involvement and those that are measurable by standard T Cell criterial. These patients require failure of at least one prior systemic therapy for the transformed lymphoma. Exclusion Criteria: The subject must be excluded from participating in the trial if the subject: 1. Is currently receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks of the first dose of treatment. 2. Has a diagnosis of immunodeficiency, is receiving systemic steroids above physiologic dose (\>10mg/day prednisone or equivalent) within 5 half lives after the last dose of steroid of start of therapy or is receiving any other form of immunosuppressive therapy. 3. Has a known history of active TB (Bacillus Tuberculosis) 4. Hypersensitivity to pembrolizumab or any of its excipients. 5. Has had a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier. 6. Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to a previously administered agent. * Note: Subjects with ≤ Grade 2 neuropathy are an exception to this criterion and may qualify for the study. * Note: If subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy. 7. Has a known additional malignancy that is progressing or requires active treatment within the last 3 years Exceptions include basal cell carcinoma of the skin, resected renal cell cancer or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer. 8. Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment. This exception does not include carcinomatous meningitis which is excluded regardless of clinical stability. 9. Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. 10. Has known history of non-infectious pneumonitis that required systemic steroid use, or has active pneumonitis. 11. Has an active infection requiring systemic therapy. 12. Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator. 13. Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. 14. Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment. 15. Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent. 16. Has a known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies). 17. Has known active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA \[qualitative\] is detected). 18. Baseline EKG shows QTcF \> 470 msec 19. Concomitant use of strong CYP3A4 inhibitors and inducers. 20. Has received a live vaccine within 30 days of planned start of study therapy. Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist®) are live attenuated vaccines, and are not allowed. 21. Has undergone prior allogenic hematopoietic stem cell transplantation any time.