This is a multicenter, double-blind, Long-Term Extension (LTE) study to evaluate the long-term safety and efficacy of APG777 in patients with moderate-to-severe AD who have completed treatment in an APG777 Parent Study (NCT06395948). The LTE study will consist of 3 periods: 1) Screening Visit will coincide with the last visit of the Maintenance Period in the Parent Study 2) Extended Treatment Period 3) Post-treatment Follow-up Period. This study will be conducted in participants with atopic dermatitis (AD) who completed the Treatment Period in a prior APG777 study and who, in the opinion of the Investigator, would benefit from long-term treatment with APG777.