T- and NK-cell lymphomas (TCL) are a heterogenous group of lymphoid malignancies with poor prognosis. In contrast to B-cell and myeloid malignancies, there are few preclinical models of TCLs, which has hampered the development of effective therapeutics. Here we establish and characterize preclinical models of TCL. We identify multiple vulnerabilities that are targetable with currently available agents (e.g., inhibitors of JAK2 or IKZF1) and demonstrate proof-of-principle for biomarker-driven therapies using patient-derived xenografts (PDXs). We show that MDM2 and MDMX are targetable vulnerabilities within TP53-wild-type TCLs. ALRN-6924, a stapled peptide that blocks interactions between p53 and both MDM2 and MDMX has potent in vitro activity and superior in vivo activity across 8 different PDX models compared to the standard-of-care agent romidepsin. ALRN-6924 induced a complete remission in a patient with TP53-wild-type angioimmunoblastic T-cell lymphoma, demonstrating the potential for rapid translation of discoveries from subtype-specific preclinical models.