The proliferation of smartphone devices has led to the emergence of powerful user services from enabling interactions with friends and business associates to mapping, finding nearby businesses and alerting users in real-time. Moreover, users do not realize that continuously sharing their trajectory data with online systems may end up revealing a great amount of information in terms of their behavior, mobility patterns and social relationships. Thus, addressing these privacy risks is a fundamental challenge. In this work, we present $TP^3$, a Privacy Protection system for Trajectory analytics. Our contributions are the following: (1) we model a new type of attack, namely 'social link exploitation attack', (2) we utilize the coresets theory, a fast and accurate technique which approximates well the original data using a small data set, and running queries on the coreset produces similar results to the original data, and (3) we employ the Serverless computing paradigm to accommodate a set of privacy operations for achieving high system performance with minimized provisioning costs, while preserving the users' privacy. We have developed these techniques in our $TP^3$ system that works with state-of-the-art trajectory analytics apps and applies different types of privacy operations. Our detailed experimental evaluation illustrates that our approach is both efficient and practical.