Recently, the subclass of starlike functions associated with exponential function e z , given by S * e = {f (z) ∈ S : zf ′ (z)/f (z) ≺ e z , (z ∈ D)} was introduced and studied by Mendiratta et al. [16]. In this article, we obtain sharp bound for third Hankel determinant for the class S * e , by improving the already known results, in this direction. In our methodology, we use the newly obtained expression for the fourth coefficient of Carathéodory functions. Univalent functions; Starlike functions; Hankel determinant; Sharp bound; Exponential function.