In this paper, we propose a novel Privacy-Preserving clearance mechanism for Local Energy Markets (PP-LEM), designed for computational efficiency and social welfare. PP-LEM incorporates a novel competitive game-theoretical clearance mechanism, modelled as a Stackelberg Game. Based on this mechanism, a privacy-preserving market model is developed using a partially homomorphic cryptosystem, allowing buyers’ reaction function calculations to be executed over encrypted data without exposing sensitive information of both buyers and sellers. The comprehensive performance evaluation demonstrates that PP-LEM is highly effective in delivering an incentive clearance mechanism with computational efficiency, enabling it to clear the market for 200 users within the order of seconds while concurrently protecting user privacy. Compared to the state of the art, PP-LEM achieves improved computational efficiency without compromising social welfare while still providing user privacy protection.