A Study of Zipalertinib in Patients With Advanced Non-Small Cell Lung Cancer With Epidermal Growth Factor Receptor (EGFR) Exon 20 Insertions or Other Uncommon Mutation.

Inclusion Criteria: 1. Written informed consent. 2. ≥18 years of age (or meets the country's regulatory definition of legal adult age, whichever is greater. 3. Pathologically confirmed, locally advanced or metastatic NSCLC meeting all the following criteria: Cohort A participants: * Documented EGFR ex20ins status, as determined by local testing performed at a Clinical Laboratory Improvement Amendments (CLIA) certified (United States \[US\]) or locally certified laboratory (outside the US). * Progressed on or after systemic therapy with an agent targeting ex20ins, either alone or in combination with standard platinum-based chemotherapy for the treatment of advanced disease. Participants who discontinued previous treatment due to unacceptable toxicity are eligible. i. Permitted prior ex20ins therapies include: amivantamab, sunvozertinib (DZD9008), and BLU451. Other prior ex20ins--directed treatment may be discussed with the Sponsor for eligibility assessment. * Participants with brain metastasis must be neurologically stable. Participants must have received central nervous system (CNS)-directed therapy and have no evidence of progression for at least 4 weeks after CNS-directed treatment, as ascertained by clinical examination and brain imaging (magnetic resonance imaging \[MRI\] or computed tomography \[CT\] scan) during the Screening Period. Additionally, they must be on a stable or decreasing dose of corticosteroids and/or anti-convulsant medications for at least 2 weeks prior to the first dose of study treatment. Participants with a history of uncontrolled seizures or LMD are not eligible. Cohort B participants: * Documented EGFR ex20instatus, as determined by local testing performed at a CLIA-certified (US) or locally certified laboratory (outside the US). * Participants who have not received prior treatment for advanced or metastatic disease and who are not appropriate candidates for first-line doublet platinum-based chemotherapy based on Investigator judgment or has refused first-line doublet platinum-based chemotherapy following discussion with the Investigator. Prior adjuvant/neoadjuvant treatment for early-stage disease must have been completed \>6 months prior to the first dose of study treatment. * Participants with brain metastasis must be neurologically stable. Participants must have received CNS-directed therapy and have no evidence of progression for at least 4 weeks after CNS-directed treatment, as ascertained by clinical examination and brain imaging (MRI or CT scan) during the Screening Period, and they must be on a stable or decreasing dose of corticosteroids and/or anti-convulsant medications for at least 2 weeks prior to the first dose of study treatment. Participants with history of uncontrolled seizures or LMD are not eligible. Cohort C participants: * Documented ex20ins or other uncommon single or compound EGFR non-ex20ins status, as determined by local testing performed at a CLIA-certified (US) or locally certified laboratory (outside the US). * Presence of brain metastasis(es) characterized as at least one of the following: * Newly diagnosed and/or progressive brain metastasis(es) measurable by Response Assessment in Neuro-oncology Brain Metastases (RANO-BM) criteria and not subjected to CNS-directed therapy, AND/OR * LMD measurable or non-measurable by RANO-BM criteria and confirmed by a positive cerebrospinal fluid cytology, or unequivocal radiographic and/or clinical determination. * Participants may not require other immediate CNS-directed therapy or will likely require other CNS directed anti-tumor therapy during the first cycle of study treatment, as judged by the Investigator. Cohort D participants: * Documented other uncommon single or compound EGFR non-ex20ins status (excluding C797S), as determined by local testing performed at a CLIA certified (US) or locally certified laboratory (outside the US). A list of eligible mutations will be provided in a separate document. * Participants with brain metastasis must be neurologically stable. Participants must have received CNS-directed therapy and have no evidence of progression for at least 4 weeks after CNS- directed treatment, as ascertained by clinical examination and brain imaging (MRI or CT scan) during the Screening Period, and they must be on a stable or decreasing dose of corticosteroids and/or anti-convulsant medications for at least 2 weeks prior to the first dose of study treatment. Participants with history of uncontrolled seizures or LMD are not eligible. * Participants who have not received prior systemic therapy for their locally advanced or metastatic NSCLC disease. * Prior adjuvant/neoadjuvant treatment for early-stage disease must have been completed \>6 months prior to the first dose of study treatment. Participants may not have received prior adjuvant/neoadjuvant treatment with any EGFR tyrosine kinase inhibitor (TKI). 4. Measurable disease per Response Evaluation Criteria in Solid Tumors version 1.1 (RECIST 1.1). 5. Archival tumor tissue available for submission, with minimum quantity sufficient to evaluate EGFRmt status and, where possible, other biomarkers (details provided in a laboratory manual). Participants with insufficient tissue may be eligible following discussion with the Sponsor. 6. Eastern Cooperative Oncology Group Performance Status (ECOG PS) 0 or 17. 7. Adequate organ function, as defined by the hematologic, renal and hepatic laboratory values. 8. Women of childbearing potential (WOCBP) must have a negative serum pregnancy test prior to administration of the first dose of study treatment. Female participants are not considered to be of childbearing potential if they are post-menopausal (no menses for 12 months without an alternative medical cause) or permanently sterile (hysterectomy, bilateral salpingectomy, or bilateral oophorectomy). 9. Both males and females of reproductive potential must agree to use effective birth control during the study prior to the first dose of study drug and for 1 month after the last dose of study treatment. DDI Substudy: 1. Participant has pathologically confirmed, locally advanced or metastatic NSCLC: a. Documented EGFRmt status as determined by local testing performed at a clinical laboratory improvement amendments (CLIA) certified (US) or locally certified laboratory (outside of the US) local laboratory, defined as either one of the following EGFRmts: * ex20ins EGFRmt OR * other uncommon, non-ex20ins EGFRmt (eg, G719X, L861Q, or S768I) OR * common EGFRmt (eg, ex19del or L858R) 2. Participant has progressed on or after receiving prior standard of care (SoC) systemic therapy for their locally advanced or metastatic NSCLC disease unless: * Participant for whom no approved therapy with demonstrated clinical benefit is indicated or available, * Participant is intolerant to the available first-line (1L) SoC treatment options, OR * Participant has refused 1L SoC treatment options (after being appropriately informed of the treatment options, risks, and benefits). 3. Participants with brain metastasis are eligible if they fulfill all of the criteria below: * Have received CNS-directed therapy and have no evidence of progression for at least 4 weeks after CNS- directed treatment, as ascertained by brain imaging (MRI or CT scan) during the Screening Period, * Are on a stable or decreasing dose of corticosteroids and/or anti-convulsant medications for at least 2 weeks prior to the first dose of study treatment, * Are neurologically stable with no history of uncontrolled seizures. 4. ECOG PS of 0 or 1. Dose Optimization Substudy: 1. Has pathologically confirmed, locally advanced or metastatic NSCLC meeting all the following criteria: 1. Documented EGFR ex20ins status, as determined by local testing performed at a CLIA certified (US) or locally certified laboratory (outside the US) 2. Progressed on or after systemic therapy standard platinum-based chemotherapy for the treatment of advanced disease. Participants who discontinued previous treatment due to unacceptable toxicity are eligible. Note: Progression on or after systemic therapy with amivantamab is permitted (eg, given as monotherapy or in combination with chemotherapy). 2. Participants with CNS metastases are eligible if both of the following criteria are met: i. Measurable lesions according to RANO-BM defined as a contrast-enhancing lesion that can be accurately measured in at least one dimension, with a minimum size of 10 millimeters (mm), or at least 5 mm if MRI slice thickness is ≤ 1.5 mm ii. Previously received definitive local treatment and have stable CNS disease (defined as being neurologically stable and off corticosteroid for at least 2 weeks prior to enrollment) OR Asymptomatic CNS metastases ≤ 2 cm in size if, in the opinion of the investigator, immediate definitive treatment is not indicated. 3. Measurable disease per RECIST 1.1. 4. Has archival tumor tissue available for submission, with minimum quantity sufficient to evaluate EGFRmt status and, where possible, other biomarkers 5. ECOG PS of 0 or 1. 6. Has adequate organ function. Exclusion Criteria: 1. Participant is currently receiving an investigational drug in a clinical trial or participating in any other type of medical research judged to be scientifically or medically incompatible with this study. 2. Has received any of the following within the specific time frame specified: 1. Participant has received Zipalertinib (TAS6417/CLN081) at any time 2. CNS radiotherapy (gamma knife radiotherapy is allowed) ≤ 12 weeks, thoracic radiotherapy ≤ 28 days, or other palliative radiation ≤ 14 days prior to the first dose of study 3. Anticancer immunotherapy ≤28 days prior to the first dose of study treatment 4. Major surgery (excluding placement of vascular access) ≤28 days prior to the first dose of study treatment. 5. Any prior treatment with an EGFR exon20ins- targeted TKI 6. Participants with leptomeningeal CNS disease. 3. Have any unresolved toxicity of Grade ≥2 from previous anticancer treatment, except for Grade 2 alopecia or skin pigmentation. Participants with other chronic but stable Grade 2 toxicities may be allowed to enroll after agreement between the Investigator and Sponsor. 4. Past medical history of interstitial lung disease, treatment-related pneumonitis (any grade), or evidence of clinically active interstitial lung disease. 5. Impaired cardiac function or clinically significant cardiac disease including any of the following: 1. History of congestive heart failure (CHF) Class III/IV according to the New York Heart Association (NYHA) Functional Classification. 2. Serious cardiac arrhythmias requiring treatment. 3. Resting corrected QT interval (QTc) \>470 msec using Fridericia's formula (QTcF). 6. Is unable to swallow tablets or has any disease or condition that may significantly affect gastrointestinal absorption of zipalertinib (eg, inflammatory bowel disease, malabsorption syndrome, or prior gastric/bowel resection). 7. History of another primary malignancy ≤2 years prior to the date of first dose of study treatment unless at least one of the following criteria are met: 1. Adequately treated basal or squamous cell carcinoma of the skin 2. Cancer in situ of the breast or cervix 3. Participants with previously treated malignancy if all treatment for that malignancy was completed at least 2 years prior to first dose and no evidence of disease 4. Participants with concurrent malignancy clinically stable and not requiring tumor-directed treatment 8. Known history of hepatitis B, hepatitis C, or human immunodeficiency virus (HIV) that is not controlled with treatment. 9. History of Coronavirus disease 2019 (COVID-19) infection within 4 weeks prior to enrollment and/or has persistent clinically significant pulmonary symptoms related to prior COVID-19 infection. 10. Active bleeding disorders. 11. Known hypersensitivity to the ingredients in zipalertinib or any drugs similar in structure or class. 12. Is pregnant, lactating, or planning to become pregnant. 13. The participant is, in the Investigator's opinion, unable or unwilling to comply with the trial procedures.