This is the chemical reaction pathway for the conversion of ZnO to ZnSO4:

ZnO $ZincOxide$ is reacted with nitric acid $HNO3$ to form Zn$NO3$2 $ZincNitrate$:
ZnO + 2HNO3 → Zn$NO3$2 + H2O

Zn$NO3$2 is then reacted with sodium hydroxide $NaOH$ to form Zn$OH$2 $ZincHydroxide$:
Zn$NO3$2 + 2NaOH → Zn$OH$2 + 2NaNO3

Zn$OH$2 is reacted with hydrochloric acid $HCl$ to form ZnCl2 $ZincChloride$:
Zn$OH$2 + 2HCl → ZnCl2 + 2H2O

ZnCl2 is then reduced to elemental Zn $Zinc$ using a reducing agent like hydrogen $H2$:
ZnCl2 + H2 → Zn + 2HCl

Finally, Zn is reacted with sulfuric acid $H2SO4$ to form ZnSO4 $ZincSulfate$:
Zn + H2SO4 → ZnSO4 + H2

Through these series of reactions, ZnO can be converted to ZnSO4.