A Trial of the FMS-like Tyrosine Kinase 3 (FLT3) Inhibitor Gilteritinib Administered as Maintenance Therapy Following Allogeneic Transplant for Patients With FLT3/Internal Tandem Duplication (ITD) Acute Myeloid Leukemia (AML)

Registration Inclusion Criteria * Participant is considered a suitable candidate for HCT and has an acceptable source of allogeneic donor stem cells, as defined per institutional practice (allogeneic HCT for any donor source \[matched sibling, unrelated donor (URD), mismatched URD, related haploidentical, or umbilical cord blood\] and any graft source \[umbilical cord, BM, peripheral blood (PB)\], and any conditioning \[myeloablative conditioning (MAC), reduced intensity conditioning (RIC), or non-myeloablative conditioning (NMA)\] will be permitted). * Participant is considered a legal adult by local regulation at the time of signing informed consent form (ICF). * Participant consents to allow access to diagnostic BM aspirate or PB sample and/or the DNA derived from that sample, if available, that may be used to validate a companion diagnostic that is being developed in parallel with gilteritinib. * Participant has confirmed, morphologically documented AML in CR1. For the purposes of registration, CR1 will be defined as \< 5% blasts in the BM with no morphologic characteristics of acute leukemia (e.g., Auer Rods) in the BM with no evidence of extramedullary disease such as central nervous system involvement or granulocytic sarcoma. * Participant has not received more than 2 cycles of induction chemotherapy to achieve CR1. The induction cycles can be the same regimen or different regimens. The regimen(s) may contain conventional agents, investigational agents, or a combin…