This article investigates the fourth Hankel determinant for N(α, γ, δ, β, η, λ, μ), the novel subclass for analytic function characterized by subordination. Estimates on a coefficients |ai| with i = 2, 3, 4, 5, 6 and 7  are provided for the functions in this recently described class, as well as an upper limit on fourth Hankel determinant. Authors asserted and demonstrated through the constructing of a new subclass of upper limits for fourth Hankel determinant of subclass for analytic function. A corollaries for main theorems provide some interesting insights, and the accompanying paper highlights the importance of the findings. These results can be used in various applications in mathematics and engineering sciences. For example, system identification, orthogonal polynomials, signal processing, approximation Theory, and this study contributes to the ability to expand our knowledge and understanding for analytical function for unit and its interactive higher relation. These findings are believed to open the doors to explorations and many future applications, not only in mathematics but also in computer science and engineering.