The purpose of this study is to evaluate the safety and efficacy of the GGTA1 KO Thymokidney in patients with end-stage renal disease (ESRD) who are either not eligible for conventional allogeneic kidney transplantation (Group 1) or are on an Organ Procurement and Transplantation Network (OPTN) kidney transplant waitlist, but are more likely to die or go untransplanted within 5 years than receive a kidney transplant (Group 2). The study consists of xenotransplantation followed by a 24-week Post-transplant Follow-up Period (Part A) to evaluate the efficacy and safety objectives followed by a Long-term Follow-up Period (Part B) to evaluate participant survival, GGTA1 KO Thymokidney survival, and screening for zoonotic infections. Part B will continue for the lifetime of the participant or for 52 weeks following nephrectomy, if required.