This paper presents a study of the phenomenon of extreme multi-stability in a novel 4D hyperjerk memristive system. The proposed system appertains to the category of dynamical systems with hidden attractors due to infinite equilibrium points. The behaviour of the system is investigated through numerical simulations, by using well-known tools of nonlinear theory, such as phase portrait, bifurcation diagram and Lyapunov exponents. Also, this work showed that the extreme multi-stability phenomenon of the behaviour of infinitely many coexisting attractors depends on the initial conditions of the variables of the system. Moreover, the case of chaos synchronisation of the system with unknown parameters, using adaptive synchronisation method, is investigated.