Fractures are frequently encountered in reservoirs used for geothermal heat extraction, CO2 storage, and other subsurface applications. Their significant impact on flow and transport requires accurate characterisation for performance estimation and risk assessment. However, fractures, and particularly their apertures, are usually associated with large uncertainties. Data assimilation (or history matching) is a well-established tool for reducing uncertainty and improving simulation results. In recent years, ensemble-based methods like the ensemble smoother with multiple data assimilation (ESMDA) have gained popularity. A key aspect of those methods is a well-constructed prior ensemble that accurately reflects available knowledge. Here, we consider a geological scenario where fracture opening is primarily created by shearing and assume a known fracture geometry. Generating prior realisations of aperture with geomechanical simulators might become computationally prohibitive, while purely stochastic approaches might not incorporate all available geological knowledge. We therefore introduce the far-field stress approximation (FFSA), a proxy model in which this stress is projected onto the fracture planes and shear displacement is approximated with linear elastic theory. We thereby compensate for modelling errors by introducing additional uncertainty in the underlying model parameters. The FFSA efficiently generates reasonable prior realisations at low computational costs. The resulting posterior ensemble obtained from our ESMDA framework matches the flow and transport behaviour of the synthetic reference at measurement locations and improves the estimation of the fracture apertures. These results markedly outperform those obtained from prior ensembles based on two naïve stochastic approaches, thus underlining the importance of accurate prior modelling.