When a chlorine atom forms an ionic bond with sodium, it gains an electron and becomes a chloride ion (Cl-). The addition of an electron increases the number of electrons surrounding the nucleus, which in turn increases the electron-electron repulsion. This repulsion outweighs the attractive force between the nucleus and the additional electron, causing the chloride ion to have a larger radius than a chlorine atom.

In other words, the chloride ion is bigger than the chlorine atom.