In this paper, we study the class A(p) which includes functions f that are meromorphic in the unit disk Δ and have a simple pole at z=p for some p∈(0,1) with the normalization f(0)=0=f′(0)-1. We establish a sufficient condition for functions in this class to be univalent. Making use of this condition, we introduce a subfamily of A(p) consisting of univalent functions satisfying a certain differential inequality in Δ. Next, we obtain a representation formula for such functions. Additionally, we establish necessary and sufficient conditions on the coefficients bn for functions f∈A(p) of the form (Formula presented.) to belong to this class. Furthermore, we determine sharp upper bounds for |bn| for all n≥2. Finally, we establish a sharp estimate for the Fekete-Szegö functional associated with the newly introduced subclass.