ABSTRACT Upcoming wide-field surveys are well suited to studying the growth of galaxy clusters by tracing galaxy and gas accretion along cosmic filaments. We use hydrodynamic simulations of volumes surrounding 324 clusters from The ThreeHundred project to develop a framework for identifying and characterizing these filamentary structures and associating galaxies with them. We define three-dimensional reference filament networks reaching 5R200 based on the underlying gas distribution and quantify their recovery using mock galaxy samples mimicking observations such as those of the WEAVE Wide-Field Cluster Survey. Since massive galaxies trace filaments, they are best recovered by mass-weighting galaxies or imposing a bright limit (e.g. >L*) on their selection. We measure the transverse gas density profile of filaments, derive a characteristic filament radius of ≃ 0.7–1 h−1Mpc, and use this to assign galaxies to filaments. For different filament extraction methods, we find that at R > R200, ∼15–$20{{\ \rm per\ cent}}$ of galaxies with M* > 3 × 109M⊙ are in filaments, increasing to $\sim 60{{\ \rm per\ cent}}$ for galaxies more massive than the Milky Way. The fraction of galaxies in filaments is independent of cluster mass and dynamical state and is a function of cluster-centric distance, increasing from ∼13 per cent at 5R200 to ∼21 per cent at 1.5R200. As a bridge to the design of observational studies, we measure the purity and completeness of different filament galaxy selection strategies. Encouragingly, the overall three-dimensional filament networks and ∼67 per cent of the galaxies associated with them are recovered from two-dimensional galaxy positions.