In this paper, we jointly study the real-time user association, traffic routing and x-Network Function (xNF) placement problem in an integrated Terrestrial and Satellite 6G Network (TN-SN), with the aim of maximizing the network energy efficiency and user acceptance ratio. We formulate the aforementioned problem as a Mixed Integer Linear Program (MILP), considering various capacity, power and flow conservation constraints for the integrated network, while also meeting the specific service requirements of each user. To tackle the increased complexity of the optimal solution, we also develop an efficient heuristic (named as TERA). Through extensive simulations, TERA demonstrates a notable superiority in energy efficiency compared to the current State-of-the-Art (SoA), achieving up to 85% of the optimal with up to 87% lower execution time even under challenging traffic load conditions.