AbstractRecent simulations and in‐situ observations have shown that magnetic reconnection is an active dissipation mechanism in the transition region of collisionless shocks. The generation mechanisms and upstream conditions enabling reconnection have been studied numerically. However, these numerical studies have been limited to the case of a steady, uniform upstream. The effect upstream discontinuities have on shock reconnection remains poorly understood. Here, we use local hybrid (fluid electron, particle ion) simulations with time‐varying upstream conditions to study the influence upstream rotational discontinuities (RDs) have on the formation of reconnected magnetic structures in the shock transition region. Our results show that bursts of reconnection can occur when RDs interact with the shock. This effect is much more significant at initially quasi‐parallel shocks than quasi‐perpendicular shocks, as the interaction between the RDs and the foreshock (only present in the quasi‐parallel case) can lead to the generation of foreshock bubbles, in which we observe an enhanced reconnection occurrence. The enhanced fluxes of accelerated ions within the foreshock bubble are likely a contributing factor to the increased reconnection occurrence. In addition, we find that the RDs with large magnetic shear are prone to reconnect upon reaching the shock, resulting in the generation of large magnetic islands. Our findings illustrate that upstream discontinuities can significantly increase the amount of reconnected magnetic structures at the bow shock, suggesting that reconnection might be a particularly important dissipation mechanism during periods of dynamic upstream conditions.