What would be the effect on the polarity of the molecule formed when CCl4 has one Cl replaced by an H?

It will become polar.

Explanation:

Look the image below. I know it's terrible, but I'll explain it:

ΔE is the electronegativity. The higher is the ΔE of a substance, the more it can attracts electrons.

Cl has more electronegativity than C and H. But it has, of course, the same amount of another Cl.

So, when we have a tetrahedral space disposition such as in the left draw, all the Cl cancels the others eletrostatic force. However, when we replace one Cl for H, then we will have a dipole moment pointing to the Cl who face the Hydrogen, as the right draw. The appearance of a resulting dipole indicates the existence of a polar compound.