There are a lot of factors to consider when making a portrait of someone: pose, expression, clothing, setting, background, etc.
As Digital Photography School points out you should also ask yourself:

1. "Where are they looking?"
2. "What impact does this have on the shot?"

For example, two people looking at each other implies a relationship and draws your viewer in.
While a subject looking outside the frame can leave the viewer wondering what they're looking at and give the photo a sense of mystery.