The present disclosure relates to polymers comprising conjugates of cyclodextrin or derivatives thereof and a linker moiety, methods of preparing the same and their application in the removal of lipids such as cholesterol from cells in treating lipid storage disorders. The present polymers exhibit improved properties including but not limiting to improved biocompatibility, improved retention time, prolonged duration of action in cells, and increased efficacy in removal of cholesterol from cells in treating lipid storage disorders.