You may consider adding dil. aq. sol. of sodium bicarbonate for conversion of dissolved zinc chloride to zinc carbonate, which should quantitatively precipitate: ZnCl2 + NaHCO3 → ZnCO3↓ + NaCl + HCl. Zinc chloride can be then regenerated from the filtered precipitate, by washing with cold water, and redissolving with aq. dil. HCl. Glycerol can be later recovered from dil. aq. mother solution by means of (e.g.) liquid-liquid extraction with tert-amyl alcohol.