Many classical clustering algorithms, like K-Means, spectral clustering, or hierarchical approaches, have been adapted to work with constraints; surprisingly, the literature completely lacks constrained versions of Random Forest Clustering (RFC) schemes, a class of methods whose usefulness has been shown in different scenarios. In this paper, we take one step to fill this gap, proposing a simple extension of RFC which works in the presence of partition-level constraints. In particular, the proposed approach exploits the modularity of RFC schemes, which all start from a Random Forest (RF) trained on available (unlabelled) data, by integrating in this first step the a priori knowledge given by the constraints, leaving the remaining part of the pipeline unchanged. We show the feasibility of our simple extension on three different RFC schemes, employing 18 datasets of small and moderate size. We also positively compare the obtained constrained RFCs with respect to some literature alternatives.