E7 TCR T Cell Induction Immunotherapy for Stage IIB-IVA Cervical Cancer

Background: * Cervical cancer is the third most common cause of death among women with gynecologic cancers in the United States. Worldwide, cervical cancer accounts for nearly 300,000 deaths annually. * Virtually all cases of cervical cancer result from chronic infection with high-risk human papillomavirus (HPV), the most common type being HPV16. * The treatment of locally advanced cervical cancer consists of chemoradiation +/- extended field radiation therapy. Participants with International Federation of Gynecology and Obstetrics (FIGO) (revised 2018) stage III-IVA have the worse prognosis with approximately 50% of the participants dying from their disease within 5 years. * Induction chemotherapy is an active area of study in this type of cancer. The aim of induction therapy is to reduce the risk of disease recurrence and improve overall survival. * E7 T-cell receptor (TCR) T cells, administered as a single infusion, have demonstrated safety and clinical activity in advanced, treatment-refractory metastatic HPV+ cancers. Objectives: -To determine the feasibility of induction E7 TCR T cell therapy for FIGO (2018) stage IIB-IVA, HPV16+ cervical cancer Eligibility: * Participants greater than or equal to 18 years old with FIGO (2018) stage IIB-IVA cervical cancer. * The cancer must be human papillomavirus 16 (HPV16+) and participant must be HLA-A\*02:01+. * Participants must be treatment-naive (i.e., no prior local or systemic treatment, including radiation; prior loop electrosurgical excision procedure (LEEP) procedure or cone biopsy is allowed). Design: * This is a single arm, pilot study, testing the feasibility of induction E7 TCR T cell therapy. * Participants will receive a conditioning regimen of cyclophosphamide and fludarabine, a single infusion of E7 TCR T cells, and systemic aldesleukin. * Participants will be referred for standard of care definitive therapy (i.e., chemoradiation +/- extended field radiation therapy) within 6 weeks after infusion of E7 TCR T cells.