Closed-loop data-driven simulation refers to the problem of finding the set of all responses of a closed-loop system to a given reference signal directly from an input/output trajectory of the plant and a representation of the controller. Conditions under which the problem has a solution are given and an algorithm for computing the solution is presented. The problem formulation and its solution are in the spirit of the deterministic subspace identification algorithms, i.e. in the theoretical analysis of the method, the data is assumed exact (noise free). The results have applications in data-driven control, e.g. testing controller's performance directly from closed-loop data of the plant in feedback with possibly different controller.