Earth system models (ESMs) are complex climate simulations that are critical for projecting future climate change and its impacts. However, running ESMs is extremely computationally expensive, limiting the number of simulations that can be performed. This results in significant uncertainty in key climate metrics estimated from ESM ensembles. We propose a Bayesian optimal experimental design (BOED) approach to efficiently calibrate ESM simulations to observational data by actively selecting the most informative input parameters. BOED optimises the expected information gain (EIG) to select the ESM input parameter to reduce the final uncertainty estimates in the climate metrics of interest. Initial results on a synthetic benchmark demonstrate our approach can more efficiently reduce uncertainty compared to common sampling schemes like Latin hypercube sampling.