A Study of Gilteritinib in Adults With Advanced ALK-positive Non-small Cell Lung Cancer (NSCLC)

Inclusion Criteria: * Participant has histologically or cytologically confirmed locally advanced or metastatic non-small cell lung cancer (NSCLC) with a documented anaplastic lymphoma kinase (ALK) rearrangement and is not amenable to curative intent treatment. * Participant is willing to submit, prior to enrollment, a fresh tumor tissue sample that was collected after completion of the most recent anti-cancer treatment and before the first dose of study intervention. If it is not medically feasible for a participant to provide a fresh tumor tissue sample, enrollment into the study should be confirmed with the Astellas medical monitor. In this case, an archival tumor tissue sample must be provided. * Participant must have at least one prior line of ALK inhibitor-based therapy and meet one of the following criteria: * Participant received alectinib as the only prior ALK inhibitor regimen. Participant is ineligible or unable to tolerate approved and available second-line therapy or is determined to potentially benefit from gilteritinib in this setting. Participant is eligible if chemotherapy was received in the neoadjuvant or adjuvant setting, and relapse or disease progressed after 12 months from completion of the treatment. * Participant received lorlatinib as one of the prior ALK inhibitor regimens. * Participant has measurable disease according to Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. * Participant has an Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 2. * Participant must have had progression or recurrence of NSCLC during or following receipt of the most recent therapy. * Female participant is not pregnant and at least 1 of the following conditions apply: * Not a woman of childbearing potential (WOCBP). * WOCBP who has a negative urine or serum pregnancy test within 7 days prior to the first dose of study intervention and agrees to follow the contraceptive guidance from the time of informed consent through at least 180 days after final study intervention administration. * Female participant must not be breastfeeding or lactating starting at screening and throughout the investigational period and for 60 days after final study intervention administration. * Female participant must not donate ova starting at the first administration of study intervention and throughout the investigational period and for 180 days after final study intervention administration. * Male participant must agree to use contraception with female partner(s) of childbearing potential (including breastfeeding partner) throughout the treatment period and for 120 days after final study intervention administration. * Male participant must agree to remain abstinent or use a condom with pregnant partner(s) for the duration of the pregnancy throughout the investigational period and for 120 days after final study intervention administration. * Male participant must not donate sperm during the treatment period and for 120 days after final study intervention administration. * Participant must meet the criteria as indicated on the clinical laboratory tests. * Participant agrees not to participate in another interventional study while receiving study intervention in the present study/participating in the present study. Exclusion Criteria: * Participant has known oncogenic driver alterations other than ALK rearrangement. * Participant has symptomatic central nervous system (CNS) metastases or leptomeningeal metastasis. * Participant has a history of malignancy other than NSCLC within 2 years before screening (exceptions are squamous and basal cell carcinomas of the skin and carcinoma in situ of the cervix or malignancy considered cured with minimal risk of recurrence). * Participant had major surgery (e.g., requiring general anesthesia) within 4 weeks prior to first dose of study intervention, or will not have fully recovered from surgery, or has surgery planned during the study treatment. * Participant has ongoing clinically significant toxicity (Grade 2 or higher with the exception of alopecia) associated with prior anti-cancer treatment. * Participant has/had febrile illness or symptomatic, viral, bacterial (including upper respiratory infection) or fungal (noncutaneous) infection within 28 days prior to first dose of study intervention. * Participant has a history of unexplained syncope, cardiac arrest, unexplained cardiac arrhythmias or torsades de pointes, structural heart disease or a family history of long QT syndrome. * Participant has a history of a cerebral vascular event (stroke or transient ischemic attack), unstable angina, myocardial infarction or cardiac symptoms (including congestive heart failure) consistent with New York Heart Association Class III-IV within 6 months prior to the first dose of study intervention. * Participant has a history of interstitial pneumonia. * Participant had completed target therapy, radiotherapy, chemotherapy, biologics and/or immunotherapy within 14 days prior to first dose of study intervention. * Participant requires treatment with strong inducers of cytochrome P450 (CYP) 3A. * Participant requires treatment with concomitant drugs that target serotonin 5HT1 or 5HT2B receptors or sigma nonspecific receptor with the exception of drugs that are considered absolutely essential for the care of the participant. * Participant has received any investigational therapy within 14 days or 5 half-lives, whichever is longer, prior to screening. * Participant has a mean Fridericia-corrected QT interval (QTcF) of \> 450 msec at screening. * Participant has known active hepatitis B virus (HBV) infection (defined as hepatitis B surface antigen (HBsAg)-positive and/or anti-HBV core antibody-positive) or known active hepatitis C virus (HCV) infection (defined as HCV RNA \[qualitative\] detected). * Participant with HBsAg-positivity and/or anti-HBV core antibody-positivity but with a negative HBV DNA PCR assay is permitted with appropriate antiviral prophylaxis or routine monitoring according to local practice. * Participant who has been curatively treated for HCV infection is permitted if he/she has documented sustained virologic response of 12 weeks. * Participant has a known history of human immunodeficiency virus (HIV) infection with acquired immunodeficiency syndrome (AIDS)-related complications. * Participant has echocardiogram (ECHO) or multigated acquisition scan (MUGA) at screening revealing left ventricular ejection fraction \< 45%. * Participant has any condition that makes the participant unsuitable for study participation. * Participant has a known or suspected hypersensitivity to gilteritinib or any components of the formulation used.