Like I said in the comments, the correlation between $x$ and $z$ may cause some issues, but that doesn't mean they are necessarily a problem for your model.
Assuming they are not perfectly correlated (in which case calculating OLS is impossible) the model as is can still be used, depending on what you want with it. If you want to make predictions on $y$, in most cases you can still do that. If you want to draw conclusions about the effect of $x$ on $y$, then you should be more careful.
Is the correlation a problem?
You can check this by checking the VIF (Variance Inflation Factor) of the variable. Most statistical software will have built-in functions to let you calculate this. If the values of the correlated variables $x$ and $z$ are higher than 5, then the correlation is starting to become a problem.
How to fix it
At the cost of introducing a bit of bias, you could drop $z$ from the model. If it is correlated enough with $x$ to become a problem for parameter-estimation, you can assume that their effects on $y$ are pretty similar, so you can just attribute all the predictive power to $x$. Alternatively you can create a new variable $w = x+z$, and use that for your regression.
More information about multicollinearity can be found here and here.