ACHIEVE - Efficacy and Effectiveness of Adoptive Cellular tHerapy wIth Ex-Vivo Expanded Allogeneic γδ T-lymphocytes (TCB008) for Patients With Refractory or Relapsed Acute Myeloid Leukaemia (AML)

Inclusion Criteria: 1. Age ≥ 18 at the time of consent 2. Karnofsky performance status ≥ 70% and WHO/ECOG performance status 0 -1 at enrolment and up to 2 at the time of infusion. 3. Must be able to remain free of systemic corticosteroid (e.g., prednisolone) and other immunosuppressive therapy at screening and for at least 5 days prior to the infusion of γδ T cells. Maintenance replacement steroid after assessment of the primary endpoint is permitted. 4. Must be able to understand and sign written informed consent and willing to participate in a clinical trial for an advanced therapy investigational medicinal product (AT(I)MP). 5. For women of childbearing potential, a urine or serum pregnancy test will be performed within 7 days prior to initiating lymphodepletion. A serum pregnancy test will be performed on the day prior to the first infusion of TCB008 (i.e. day -1) and urine or serum pregnancy tests will be performed on the day of subsequent infusions with TCB008 and the results must be negative at all times that these pregnancy tests are performed. For women of childbearing potential, a serum pregnancy test will be performed at visit 17 or early termination. Patient and his/her partner must agree to use adequate contraception from the time of providing written consent through 3 months after the last study drug dose 6. Pathologically confirmed diagnosis of AML or MDS/AML confirmed according to ELN 2022 Criteria (as per International Consensus Classification of AML). 7. For Cohort A1, patients must have AML or MDS/AML that is primary refractory defined as not achieving a CR, CRi or CRh after 2 cycles of intensive or non-intensive induction chemotherapy. 8. For Cohort A2, patients with AML or MDS/AML must have previously achieved a CR, CRi or CRh (including MRD negative CR) to previous intensive or non-intensive therapy, then have experienced relapsed AML. 9. For Cohort B, patients with AML who have achieved CR, CRi or CRh but have persistent MRD by multiparameter flow cytometry-based MRD (MFC-MRD) or molecular MRD (Mol-MRD) assessed by qPCR. Included patients will not be deprived of standard of care by participating in this trial. Exclusion criteria 1. Suspected or proven active CNS disease. 2. Previous reactions to Fludarabine or Cyclophosphamide or patients at risk of Fludarabine related neurotoxicity 3. Acute promyelocytic leukaemia 4. Bisphosphonates (≤8 weeks before study entry), unless continued as a standard of care medication 5. Corticosteroids (cumulative dose of systemic steroids \>20mg of prednisolone per day or equivalent) that cannot be discontinued 5 days prior to TCB008 infusion. 6. Antihyperlipidemic medications (e.g., statins) that cannot be discontinued prior to enrolment. 7. Cardiac failure: EF \< 40%. 8. Kidney function: creatinine clearance ≤ 60 mL/min. 9. Liver function: total bilirubin \> 3 × ULN, aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \> 5 × ULN. 10. Neurological condition(s) which might be exacerbated by therapy or prevent assessments for neurotoxicity/ICANS. 11. GVHD of any grade or anti-GVHD treatment. 12. Lung function: symptoms of respiratory failure or \< 92% oxygen saturation on air. 13. Active infections that are difficult to control, including positive COVID-19 diagnosis at screening. NOTE: Active infections following lymphodepletion may exclude a patient from being able to be dosed with IMP. 14. Received autologous or allogeneic cell therapy within 4 weeks, such as donor lymphocyte infusion. 15. Received autologous or allogeneic gene modified adoptive cell therapy (e.g. CAR-T, TCR-T, CAR-NK cell therapy, etc). 16. Subject received anti-tumour treatment (chemotherapy, monoclonal antibody, or hormone) within one week of screening (hydroxycarbamide is permitted until lymphodepletion). 17. Has a known history of prior malignancy, except for; 17.a. Malignancies that were treated curatively and have not recurred within 2 years prior to study treatment 17.b. Completely resected basal cell and squamous cell skin cancers 17.c. Any malignancy considered to be indolent and that has never required therapy 17.d. Completely resected carcinoma in situ of any type 18\. Pregnant or lactating women. 19\. Hypersensitivity to iron-dextran or murine antibodies. 20\. Patients who are active participants in other interventional clinical trials at the same time. Co-enrolment is permitted for non-interventional studies if approved by the CI. 21\. The Investigator believes that there are other factors that are not suitable for inclusion or influence the patient's participation or completion of the study. 22\. Considered unsuitable for further intensive therapy or expected to survive less than 3 months with conventional available treatments.