Place recognition is crucial for loop closure detection and global localization in robotics. Although mainstream algorithms typically rely on cameras and LiDAR, these sensors are susceptible to adverse weather conditions. Fortunately, the recently developed 4D millimeter-wave radar (4D radar) offers a promising solution for all-weather place recognition. However, the inherent noise and sparsity in 4D radar data significantly limit its performance. Thus, in this paper, we propose a novel framework called 4DRaL that leverages knowledge distillation (KD) to enhance the place recognition performance of 4D radar. Its core is to adopt a high-performance LiDAR-to-LiDAR (L2L) place recognition model as a teacher to guide the training of a 4D radar-to-4D radar (R2R) place recognition model. 4DRaL comprises three key KD modules: a local image enhancement module to handle the sparsity of raw 4D radar points, a feature distribution distillation module that ensures the student model generates more discriminative features, and a response distillation module to maintain consistency in feature space between the teacher and student models. More importantly, 4DRaL can also be trained for 4D radar-to-LiDAR (R2L) place recognition through different module configurations. Experimental results prove that 4DRaL achieves state-of-the-art performance in both R2R and R2L tasks regardless of normal or adverse weather.