Answer
The chemical formula for the conjugate acid of $Cl{O_2}^-$ is:
$HClO_2$
Work Step by Step
To find the conjugate acid of a base, you just need to add a proton $(H^+)$ to the compound.
1. Add one hydrogen.
$Cl{O_2}^- --\gt HCl{O_2}^-$
2. Add "+1" to the charge of the compound:
$-1 -- \gt 0$
$HClO{_2}^- --\gt HClO_2$