Spatiotemporal coordination of chromatin and subnuclear compartments is crucial for cells. Numerous enzymes act inside nucleus-some of those transiently link and pass two chromatin segments. Here, we study how such an active perturbation affects fluctuating dynamics of an inclusion in the chromatic medium. Using numerical simulations and a versatile effective model, we categorize inclusion dynamics into three distinct modes. The transient-link-and-pass activity speeds up inclusion dynamics by affecting a slow mode related to chromatin remodeling, viz., size and shape of the chromatin meshes.