Sensing-assisted communication is critical to enhance the system efficiency in integrated sensing and communication (ISAC) systems. However, most existing literature focuses on large-scale channel sensing, without considering the impacts of small-scale channel aging. In this paper, we investigate a dual-scale channel estimation framework for sensing-assisted communication, where both large-scale channel sensing and small-scale channel aging are considered. By modeling the channel aging effect with block fading and incorporating CRB (Cramér-Rao bound)-based sensing errors, we optimize both the time duration of large-scale detection and the frequency of small-scale update within each subframe to maximize the achievable rate while satisfying sensing requirements. Since the formulated optimization problem is non-convex, we propose a two-dimensional search-based optimization algorithm to obtain the optimal solution. Simulation results demonstrate the superiority of our proposed optimal design over three counterparts.