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In this study, by making the use of <i>q</i>-analogous of the hyperbolic tangent function and a Sălăgean <i>q</i>-differential operator, a new class of <i>q</i>-starlike functions is introduced. The prime contribution of this study covers the derivation of sharp coefficient bounds in open unit disk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>U</mi><mo>,</mo></mrow></semantics></math></inline-formula> especially the first three coefficient bounds, Fekete–Szego type functional, and upper bounds of second- and third-order Hankel determinant for the functions to this class. We also use Zalcman and generalized Zalcman conjectures to investigate the coefficient bounds of a newly defined class of functions. Furthermore, some known corollaries are highlighted based on the unique choices of the involved parameters <i>l</i> and <i>q</i>.