We propose a new Pareto Local Search Algorithm for the many-objective combinatorial optimization. Pareto Local Search proved to be a very effective tool in the case of the bi-objective combinatorial optimization and it was used in a number of the state-of-the-art algorithms for problems of this kind. On the other hand, the standard Pareto Local Search algorithm becomes very inefficient for problems with more than two objectives. We build an effective Many-Objective Pareto Local Search algorithm using three new mechanisms: the efficient update of large Pareto archives with ND-Tree data structure, a new mechanism for the selection of the promising solutions for the neighborhood exploration, and a partial exploration of the neighborhoods. We apply the proposed algorithm to the instances of two different problems, i.e. the traveling salesperson problem and the traveling salesperson problem with profits with up to 5 objectives showing high effectiveness of the proposed algorithm.