This paper introduces coefficient functionals for a new subclass (Stanh*) of starlike functions associated with the tangent hyperbolic function, including the first four sharp coefficient bounds, the Fekete-Szegő problem, Zalcman inequalities, and Hankel determinants. For this class, logarithmic and inverse problems are also studied. Furthermore, we define families of functions that are related to the functions 1+sinμ,1+αμ2,1+μ1−βμ2, represented by Ysin,Yα and Yβ, respectively. Using the Schwarz-Pick lemma and the theory of subordination, involving the function 1+12tanhμ, we find the majorization radii and construct majorization results of the form g′μ≤h′μ for functions g majorized by h. Through graphical analysis, we also demonstrate that our defined class Stanh* is non-empty, which validates our study in this article.