Was that character supposed to be a burn victim? His makeup effects look like the Klingon version of that mama cat that ran back into a house fire repeatedly to rescue her kittens and she kind of melted.
Chang's appearance, as well as his affection for the works of the Human playwright Shakespeare, may be explained in part by the Klingon augment virus that spread through the Empire in the mid-22nd century. Among its other effects, the virus dissolved Klingon cranial ridges and gave its victims a more Human appearance (see "Affliction"). One of Chang's ancestors may have been a "smooth-headed" Klingon who was exposed to the retrovirus. Also, he lost an eye and wore a eyepatch similar to Claus von Stauffenberg.
But mostly, Christopher Plummer didn't want to put up with bulky makeup.