Just use samples from the posterior of the parameters!
So after you fit your model in PyMC, write a loop that takes one sample from the trace for a and b, drops those samples into your next function for y', and calculate to get a single output. Repeat that process to get samples from the pdf of y'.
You can get the same result by setting y' as a “deterministic” in your model, something like
pm.Deterministic("y_prime", a + c * x_prime + exp(b*x_prime))
and then you’ll find y_prime in your trace or idata object with the other parameters you fit.