The paper describes the method of symbolic evaluation that serves as a useful tool to extend the studies of certain special functions including their properties and capabilities. In the paper, we exploit certain symbolic operators to introduce a new family of special polynomials, which is called the Mittag-Leffler-Gould-Hopper polynomials. We obtain the generating function, series definition and symbolic operational rule for these polynomials. This approach give a wide platform to explore the study of classical and hybrid special polynomials. We establish summation formulae and certain identities for these polynomials. Further, we derive the multiplicative and derivative operators to study the quasi-monomiality property of these polynomials. Some concluding remarks are also given.