Gaze estimation is the task of deciding for given face images, in which direction people are looking. It is particularly useful for various applications including psychological analysis, authentication, and eye tracking in the context of virtual or augmented reality. To reduce the error of the predictions of gaze estimators, the training data should be collected from a large number of users to ensure the ability of the model to generalize correctly during the inference phase. However, the large data collection requirements conflict with privacy concerns. Building on existing federated learning approaches, this project aims to increase the efficiency of the training process. Hence, (i) we split the model into a part owned by the client and another part owned by a server. This results in strong data protection properties as well as model privacy. In addition, only a part of the model has to be stored and run by each client leading to decreasing computational effort for the typically substantially resource-constrained clients. (ii) We further train the gaze estimation model in an unsupervised fashion and (iii) prune the model weights to enhance the training efficiency. Furthermore, we extend our approach with several privacy-preserving techniques, e.g. Multi-Party Computation (MPC) and Differential Privacy (DP) mechanisms. We empirically demonstrate the effectiveness of these mechanisms with an implemented attack on our system. Our experiments show that our implemented system manages to predict gaze angles with an average deviation of less than 6.5 degrees from the actual angle in about 10 minutes and thus outperforms other privacy-preserving gaze estimators.