In this paper we introduce a new class of sets namely *gs-closed sets which settled in between the class of g*-closed sets²² and the class of gs-closed sets¹³ then we study many basic properties of *gs-closed sets together with the relationship of these sets with some other sets. Applying these sets we introduce and study new class of spaces namely T_s-spaces, T_s*-spaces and *T_s-spaces. Further we introduce and study *gs-continuous maps and *gs-irresolute maps. Finally we introduce the concept of *gs-compactness and *gs-connectedness in topological spaces and study some of their properties.