In this present paper, as applications of the post-quantum calculus known as the $(p,q)$-calculus, we construct a new class $\boldsymbol{D}_{p,q}^{k}\left( \gamma ,\zeta ,\Psi \right) $ of bi-univalent functions of complex order defined in the open unit disk. Coefficients inequalities and several special consequences of the results are obtained.