Is mercury covalent or ionic bond?

Mercury ions are cations. Chloride ions are anions.

"In an ionic bond, the atoms are bound together by the attraction between oppositely-charged ions. In a covalent bond, the atoms are bound by shared electrons."

1 mercury ion loses 2 electrons to 2 chloride ions (i.e. 1 electron to 1 chloride ion), thus forming an ionic compound MgCl2.