The charm sector offers considerable scope for exploring new physics (NP) beyond standard model (SM). In this work, we look for possibilities of NP due to the effects of \(Z'\) boson on the rare charm decays \(D\rightarrow \rho e^+ e^-\) , which proceed through \(c\rightarrow u l^+ l^-\) quark transition. The \(Z'\) boson couples with both quarks and leptons. We modify the Wilson coefficients by incorporating the NP couplings. We estimate the branching fractions and forward-backward asymmetries in the \(Z'\) model and compare them with their corresponding SM values. Since \(D \rightarrow \rho e^+ e^-\) decays are FCNC decays undergoing \(c\rightarrow u l^+ l^-\) transition, we expect these decays to be sensitive to the effects of the \(Z'\) boson.