It is practically impossible to remove chlorides from the solution. In the case of zinc metallurgy, the treatment of zinc oxide, obtained e.g. from the Waelz process, is used to remove chlorides and fluorides from it. After purification, the oxide can be leached with sulfuric acid and the resulting solution no longer contains chlorides or fluorides. I have attached articles on how to remove unwanted compounds from ZnO.

There are two common methods to produce a solution with lower Cl, one is to precipitate the zinc (and other metals) with caustic or carbonate, use a filter to recover the precipitate and then re-dissolve the zinc with acid solution with low

Cl water, typically demineralised water. The second option is to extract the zinc using ion exchange or solvent extraction and strip the zinc from the organic extractant or resin into a a low chloride solution.

Both options mean that a base is required to neutralise the acid associated with the metal ion, you don't need to do this for all of the zinc solution but only enough to meet your Cl target.

It is preferable to limit the chloride ingress into the leach solution, this could be by washing the ore/concentrate prior to leaching in a low chloride solution, or evaluating water quality used in the leaching process, especially if leach solution is recycled then chloride levels will increase to an equilibrium level, a bleed stream may be a good way to manage the chloride levels...