A novel multi-fidelity approach of both turbulence and geometry is developed to study the tailing edge cutback flows. Large-eddy simulation is zonalised around the blade trailing edge to predict coolant mixing, while the Immersed Boundary Method (IBM) is used for modelling pin fins in the upstream internal passage. This reduces the overall computational cost while retaining the high-fidelity solution in the region of interest and allowing the parametric study of pin-fin geometry and arrangement without generating new meshes. The multi-fidelity approach has been fully validated with the experimental data and then demonstrated to study the effects of pin-fin shapes on the unsteady cutback flows and cooling performance.