A Study to Evaluate Safety, Tolerability, Pharmacokinetics, and Pharmacodynamics of Zampilimab in Adult Kidney Transplant Recipients With Chronic Allograft Injury

Inclusion Criteria: * Functioning living or deceased donor allograft \>=1 year post-transplantation * Baseline (screening) biopsy showing Grade II or III interstitial fibrosis/tubular atrophy (IF/TA) (\>=25% IF/TA) * Progressive loss in kidney function observed after the first year post-transplant, defined as an estimated glomerular filtration rate (eGFR) decline of ≥3 mL/min/year for at least 24 months prior to screening, with a minimum of 2 documented measurements per year (minimum of 4 documented measurements in the 24-month period, performed at least 1 month apart) * An eGFR \>=30 mL/min/1.73 m\^2 for a period of 6 months up to screening * Stable standard of care concomitant medication for 3 months prior to screening * Participant is male or female, \>=18 years of age Exclusion Criteria: * Recipient of multi-organ transplant (with the exception of repeated kidney transplant recipients, and/or corneal transplant recipients) * Screening biopsy shows evidence of significant active antibody-mediated rejection that may affect the conduct of the study (eg, require change in treatment) according to the Principal Investigator (PI) * Screening biopsy shows evidence of T cell-mediated rejection that may affect the conduct of the study (eg, require change in treatment) according to the PI * Screening biopsy shows evidence of de novo or recurrent glomerular disease that may affect the conduct of the study (eg, require change in treatment) according to the PI * Proteinuria ≥1500 mg/g at screening * Participant who has a history of biopsy-proven acute rejection or treatment for suspected acute rejection within 3 months prior to screening * Participant has had major surgery (including joint surgery) within 6 months prior to screening, or has planned surgery within 6 months after the last dose of investigational medicinal product (IMP) * Participant has a current diagnosis of foot ulcer or diagnosis of chronic diabetic ulcer or history of delayed wound healing * Participant has taken concomitant medication of sirolimus or everolimus within 3 months of screening