In the present work we study theoretically hydrogen incorporated into several positions in the zirconia cubic and tetragonal lattices. These are positions in the interstitial space and in the zirconium vacancy (V
Zr). We examine the structure of such configurations and for V
Zr-related defects we also calculate selected positron characteristics in order to assess their capability of trapping positrons. It is shown that hydrogen atoms do not prefer to stay in the center of the largest interstitial space nor of V
Zr and they rather tend to create bonds with neighboring oxygen atoms. The positron lifetime of the VZr+1H complex is shorter than that for non-decorated V
Zr and positron trapping in V
Zr+1H complexes could, in principle, explain experimental lifetime data.