AZD4205 in Relapsed or Refractory Peripheral T Cell Lymphoma (JACKPOT27)

Inclusion criteria: 1. ≥ 18 years old (for Korean ≥ 19 years old) 2. ECOG performance status 0-2 with no deterioration over the previous 2 weeks 3. Predicted life expectancy ≥ 12 weeks. 4. Histologically confirmed PTCL by local pathology review according to the 2016 revision of the WHO classification of lymphoid neoplasms. Eligible histological subtypes are restricted to the following: * PTCL-NOS * AITL * ALCL ALK+ * ALCL ALK- * EATL * MEITL * NKTCL * HSTCL * SPTCL 5. Have measurable disease according to the 2014 Lugano classification 6. Must have progressed on or are refractory to standard systemic therapy, or patients were intolerant to standard systemic therapy. Participants should be transplant-ineligible upon their entries to this study. 7. Adequate bone marrow reserve and organ system functions 8. LVEF ≥ 55% assessed by ECHO or MUGA. 9. Male participant with female partners of child-bearing potential should be willing to use barrier contraceptives (i.e., by use of condoms), during his participation in this study and for 6 months following the last dose of the study drug. Male participant must refrain from donating sperm during their participation in the study and at least for 6 months after the last treatment. 10. Female participant should be using adequate contraceptive measures while on study drug and for 3 months following the last dose of study drug. Exclusion criteria: 1. Intervention with any of the following: * Any investigational agents or study drugs from a previous clinical study within 30 days of the first dose of study treatment. * Any cytotoxic chemotherapy from a previous treatment regimen within 21 days of the first dose of study treatment. * Prior HDAC inhibitors (including romidepsin, belinostat and chidamide) or pralatrexate therapy within one week of the start of the study treatment. * Corticosteroids at dosages equivalent to prednisone \> 15 mg/day within 7 days of the start of the study treatment. * Major surgery procedure (excluding placement of vascular access), or significant traumatic injury within 4 weeks of the first dose of study treatment, or have an anticipated need for major surgery during the study. * Prior therapeutic anticancer antibodies (including brentuximab vedotin) within 4 weeks, other radio- or toxin-immunoconjugates within 10 weeks, radiation therapy within 3 weeks. * Has undergone an allogeneic stem cell transplant. Participant had autologous stem cell transplant within 6 months. * Prior treatment with a JAK or STAT3 inhibitor. * Prior treatment with any onco-immunotherapy in 28 days prior to first dosing of AZD4205. * Live vaccines within 28 days prior to first dose. * Currently receiving (or unable to stop use at least 1 week prior to receiving the first dose) vitamin K antagonists, anti-platelet agents or anticoagulated agents. * Currently receiving (or unable to stop use at least 1 week prior to receiving the first dose) medications or herbal supplements known to be potent inhibitors or inducers of CYP3A or sensitive substrates of BCRP or P-gp with narrow therapeutic index. 2. Any unresolved toxicities from prior therapy, greater than CTCAE v 5.0 Grade 1 at the time of starting study treatment with the exception of alopecia. 3. Central nervous system or leptomeningeal lymphoma. 4. With severely decreased lung function (i.e. any parameter of FEV1, and DLCO \< 60% of predicted value). Past medical history of pneumonitis, drug-induced interstitial lung disease, radiation pneumonitis which required steroid treatment, or any evidence of clinically active interstitial lung disease. 5. With disease condition which requires the treatment of immunosuppressants, biologics, or NSAIDs (non-steroid anti-inflammatory drugs). 6. Active infections including: * History of known latent or active tuberculosis (TB). * Known infection with HIV, or serologic status reflecting active hepatitis B or hepatitis C infection. * Active viral infections (i.e. zoster) other than hepatitis B or C. * Infections requiring oral or intravenous antimicrobial therapy or interferon. * Bacterial infections including pneumonia within 30 days. 7. Any of the following cardiac criteria: * Congestive heart failure (CHF) per NYHA classification \> Class II. * Clinically significant valvular diseases, hypertrophic or constrictive cardiomyopathy. * Any clinically significant abnormalities in rhythm, conduction or morphology of resting ECG, e.g., complete left bundle branch block, third degree heart block, and second-degree heart block, PR interval \> 250 msec. * Cardiac ventricular arrhythmias requiring anti-arrhythmic therapy. * AMI within 6 months prior to starting treatment, unstable angina or new-onset angina. * With heart transplant. * Mean resting corrected QTcF interval (QTC) \> 450 ms on ECG. * With factors that increase the risk of QT prolongation or arrhythmic events (e.g., heart failure, hypokalaemia, congenital long QT syndrome, any concomitant medication known to prolong the QT interval) or family history of long QT interval syndrome or unexplained sudden death under 40 years of age in first degree relatives. * With previous/current thrombotic diseases such as pulmonary embolism, and deep venous thrombosis. 8. Another malignancy within 5 years prior to enrollment with the exception of adequately treated in-situ carcinoma of the cervix, uterus, basal or squamous cell carcinoma or non-melanomatous skin cancer.