The iris' primary function is to regulate the size of the pupil, thereby controlling the amount of light entering the eye. I don't see any reason why it couldn't be much larger than our irises tend to be.
On a related note, humans are somewhat unique in that our sclera (the "white" of the eye) is easily visible and stands out in contrast to the darker iris. This appears to be an evolutionary development related to the kind of cooperative efforts necessary for human society to thrive.
In short, we have smallish, dark irises and large, white scleras because it allows us to determine where other people are looking, without having to ask or rely on observing the other person's head movements. Studies have shown that infant humans tend to follow eye direction without additional head movement more often than they follow head movement, with or without eye movement. Other primates, however, ignore movements of the eyes alone, but do follow head movements.
So your alien species can have huge irises and hidden scleras as long as they don't need to follow subtle eye movements which are not accompanied by head movements.