The stress element shows all possible stresses that could act at a point in a solid body, but suppose we know that a state of plane stress exists at the point.
How will this illustration change?

If a point is subjected to plane stress, then all stress components that act in the $z$ direction must be zero.

Therefore, ${\tau }_{yz}$ must equal zero...

...and since ${\tau }_{zy}$ must equal ${\tau }_{yz}$ to satisfy equilibrium, we can conclude that ${\tau }_{zy}=0$.