Non-small cell lung cancer (NSCLC) is a type of lung cancer. Some people with NSCLC have a faulty gene called ALK, which stands for anaplastic lymphoma kinase. This study is for people whose cancer stopped responding to ALK inhibitor treatments. The study will test a drug called gilteritinib, already used for another cancer type, to see if it helps people with ALK-positive NSCLC.

Participants will take gilteritinib pills once a day in 28-day cycles. Regular tumor scans will be done to check progress. They will stay in the study for up to 4 years, depending on their response to the drug. Visits to the clinic are required after stopping the drug for safety checks and reports on health will continue every 12 weeks.

• The study lasts up to 4 years, with regular clinic visits and scans.
• Participants will take daily pills of gilteritinib.
• Eligibility: Cannot have recent surgeries, certain heart conditions, or brain cancer symptoms.