This Phase 2b open-label, long-term extension study is designed to evaluate the long-term safety and efficacy of KT-621 in participants with asthma who were previously enrolled in the parent study (KT621-AS-202) of KT-621 for asthma. The main goals of this study are to investigate the long-term safety and tolerability of KT-621, the long-term efficacy of KT-621 at treating asthma, and how KT-621 behaves in the body long-term.

Inclusion Criteria:

• Must have completed all visits of the parent study, per its protocol, up to the end of treatment (EoT) visit.
• Must be willing and able to comply with scheduled visits, treatment plan, laboratory tests, other study-related procedures, and questionnaires, including completing the electronic diary (e-diary), for the duration of the study as required by the study protocol.
• Must agree to contraceptive requirements in compliance with the clinical study and local requirements.

Exclusion Criteria:

• Must not have experienced any clinically significant change in health status during the parent study, which, in the opinion of the Investigator, would interfere with participant safety, study evaluations, or compliance with study procedures; or otherwise make the participant unsuitable for participation in this study.
• Must not have developed an AE during the parent study, that in the opinion of the Investigator or of the Sponsor's Medical Monitor, could indicate that continued treatment may present an unreasonable risk for the participant.
• Must not have met permanent discontinuation criteria and/or permanently discontinued study treatment for any reason during the parent study.
• Must not be a member of the Sponsor or site's investigational team or their immediate family.
• Must not be unsuitable to enter the study for any other reason, as judged by the Investigator, including potential risk of noncompliance to study procedures.