Longman and Cambridge just say, pretty much, the same as the dictionary definition you posted: ire - Definition from Longman English Dictionary Online - Cambridge Dictionaries Online - Cambridge University Press.
It seems as though "ire" has its limitations, though I wouldn't say this is conclusive. It just kind of seems that way. A collocation dictionary might be useful if you have one. I have the Longman Language Activator, though at a glance, I didn't see anything about "ire" there.
Then again, you could just check Google to see what people write and say: "incur the ire" - Google Search=
Some people don't think Google is useful in this way, but I disagree. Google is useful in this way.