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

Primary Objectives: 1. Evaluate the safety of pembrolizumab in combination with romidepsin. 2. Estimate the response rate of the combination therapy in refractory or recurrent PTCL Secondary Objectives: 1. Estimate progression free survival (PFS). 2. Estimate overall survival (OS). 3. Estimate complete response (CR) and duration of response (DOR). 4. Estimate the event-free survival (EFS) and the failure free survival (FFS) 5. Estimate the overall response rate (ORR) per Lugano criteria. Exploratory Objectives: 1. Assess activation of T-cells after treatment in peripheral blood and tumor microenvironment. 2. Correlate features of peripheral blood T-cell activation with toxicities, clinical response, and PFS. OUTLINE: Participants receive romidepsin intravenously (IV) over 4 hours on days 1 and 8 or day 8 of cycle 1 and days 1 and 8 of subsequent cycles and pembrolizumab IV over 30 minutes on day 1. Cycles repeat every 21 days for up to 36 cycles in the absence of disease progression or unacceptable toxicity. After completion of study treatment, participants are followed up at 30 days and then every 12 weeks.