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Subhalo dynamics in galaxy cluster host halos govern the observed distribution and properties of cluster member galaxies. We use the IllustrisTNG simulation to investigate the accretion and orbits of subhalos found in cluster-size halos. We find that the median change in the major axis direction of cluster-size host halos is approximately 80° between a ∼ 0.1 and the present day. We identify coherent regions in the angular distribution of subhalo accretion, and ∼68% of accreted subhalos enter their host halo through ∼38% of the surface area at the virial radius. The majority of galaxy clusters in the sample have ∼2 such coherent regions. We further measure angular orbits of subhalos with respect to the host major axis and use a clustering algorithm to identify distinct orbit modes with varying oscillation timescales. The orbit modes correlate with subhalo accretion conditions. Subhalos in orbit modes with shorter oscillations tend to have lower peak masses and accretion directions somewhat more aligned with the major axis. One orbit mode, exhibiting the least oscillatory behavior, largely consists of subhalos that accrete near the plane perpendicular to the host halo major axis. Our findings are consistent with expectations from inflow from major filament structures and internal dynamical friction: most subhalos accrete through coherent regions, and more massive subhalos experience fewer orbits after accretion. Our work offers a unique quantification of subhalo dynamics that can be connected to how the intracluster medium strips and quenches cluster galaxies.