First we should know about that Semiconductor in which you are going to dope Zr, whether it is a p-type or n-type semiconductor. Then it can be guessed that how much doping will shift its band edge to lower or higher energy.
The question is still to general. For example, substitutional Zr doping of SrTiO3 increases the band gap, e.g. Jahangir-Moghadam, Chambers, Ngai et al., DOI: 10.1002/admi.201400497 and Weston, Van de Walle et al., DOI: 10.1103/PhysRevB.92.085201