Memory Alpha:

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.