This paper introduces an Adaptive Mesh Refinement (AMR) methodology for Topology Optimization (TO) of fourth-order plate structures using Isogeometric PHT-Splines. We focus on the benefit of Isogeometric Analysis (IGA) to inherently discretize the \(C^1\) continuous weak form of plate structures. Our approach offers several advantages over traditional methods, including a discrete density field for the material distribution filtered through a first-neighbourhood strategy and a hierarchical tree structure for the structural mesh that enables effortless implementation of an AMR strategy. Utilizing the Geometry Independent Field approximaTion (GIFT), we discretized the design and adaptive analysis stages independently through NURBS and PHT-Splines, respectively, enabling easy transfer of geometries from industry-standard packages. Numerical examples demonstrate the superiority of our proposed methodology over traditional methods in terms of solution accuracy and computational efficiency.