Given a right-angled Artin group (RAAG), Kim-Koberda developed a method for constructing quasi-isometrically embedded subgroups that are themselves RAAGs. Independently, similar constructions were developed for mapping class groups by Clay-Leininger-Mangahas and Runnels. In this talk, we will present a method for finding right-angled Artin subgroups within hierarchically hyperbolic groups-a unified framework that includes both RAAGs and mapping class groups. This approach offers a common perspective on subgroup embeddings across these important classes of groups.