This paper investigates the new coupled (2 + 1)-dimensional Zakharov–Kuznetsov (ZK) system with time-dependent coefficients for multiple types of exact solutions by using the Lie symmetry transformation method.Similarity transformation reduces the system of equations into ordinary differential equations and further, these are solved for solutions having bright, dark and singular solitons as well as periodic waves. Also, the solutions appeared in terms of time-dependent coefficient $\beta(t)$ and analysed graphically to show the effect of this arbitrary function. It is proved that the given system is nonlinear self-adjoint, and some conservation laws are obtained by applying the new conservation theorem.