How can electron move between two metals without the presence of electric field? Electron can move from one location to another if it feels a force that is if there is a presence of electric field. Now suppose I have a $\ce{Zn}$ rod immersed in $\ce{CuSO4}$ solution. Electrons are transferred from $\ce{Zn}$ to $\ce{Cu}$. What results in this motion of electrons from $\ce{Zn}$ to $\ce{Cu}$. How can electron move without a field?
The wording of the question hides the answer.

Electrons do not move from Zn to Cu. They move from neutral zinc to cupric ion Cu++. The field arises from the mix of H2O, H+, OH-, SO4--, and Cu++ all around the Zn rod. Could electrons be forced onto Zn from OH- or SO4-- ? No.There is no gain in stability; energy would be needed. Or could electrons be attracted to H+; yes, and even more so to Cu++. And the final products (Zn++ and neutral Cu) would be more stable.