Clustered cell-free networks have emerged as a promising architecture for sixth generation ultra-dense wireless communication systems by enabling local cooperation among base stations while controlling system complexity. For resource allocation and performance optimization of such networks, accurate and efficient estimation of the ergodic achievable downlink rate is a fundamental prerequisite. Existing rate estimation approaches mainly rely on computationally prohibitive Monte Carlo simulations or adopt random matrix theory-based methods, which have been well-developed for conventional cellular and cell-free networks. However, existing RMT-based methods have not addressed the unique inter-subnetwork interference in clustered cell-free networks, and therefore lack an efficient solution for accurate downlink rate estimation under both regularized zero-forcing and zero-forcing precoding. In this paper, we propose a stabilized element-wise rate estimation method for downlink rate estimation in clustered cell-free networks. We establish the diagonal element-wise convergence of resolvent matrices, which enables the derivation of deterministic equivalents for inter-subnetwork interference and the downlink ergodic rate. We further introduce a stabilized variable transformation to address the numerical instability when the regularization parameter is very small, hereby enabling a unified formulation applicable to both regularized zero-forcing and zero-forcing precoding. Simulation results show that the proposed method achieves a relative error below 6% while significantly reducing computational complexity compared with the Monte Carlo simulation.