How HCl when mixed in water conduct electricity though it(HCl)is a covalent bond?

HCl is a polar covalent molecule with a partial positive charge on hydrogen (H⁺) and a partial negative charge on chlorine (Cl^-).

When this is dissolved in water, water too being a polar molecule with a partial positive charge on hydrogen (H⁺) and a partial negative charge on oxygen (O^2-), hydrogen of HCl are surrounded by oxygen of water forming dipole dipole bonds.

HCl + H₂O  →  H₃O⁺ + Cl^-

When the dipole-dipole bond is formed, the original bond between H and Cl weakens and ultimately breaks leading to ionization.

Molecules are called electrically conductive if they form ions, when dissolved in water.

For HCl,

HCl + H₂O  →  H₃O⁺ + Cl^-

Hence, HCl when mixed in water conduct electricity though it (HCl) is a covalent bond.