Gaze estimation across domains has been explored recently because the training data are usually collected under controlled conditions while the trained gaze estimators are used in real and diverse environments. However, due to privacy and efficiency concerns, simultaneous access to annotated source data and to-be-predicted target data can be challenging. In light of this, we present an unsupervised source-free domain adaptation approach for gaze estimation, which adapts a source-trained gaze estimator to unlabeled target domains without source data. We propose the Uncertainty Reduction Gaze Adaptation (UnReGA) framework, which achieves adaptation by reducing both sample and model uncertainty. Sample uncertainty is mitigated by enhancing image quality and making them gaze-estimation-friendly, whereas model uncertainty is reduced by minimizing prediction variance on the same inputs. Extensive experiments are conducted on six cross-domain tasks, demonstrating the effectiveness of UnReGA and its components. Results show that UnReGA outperforms other state-of-the-art cross-domain gaze estimation methods under both protocols, with and without source data