"Get over his/herself" might be the best answer given so far. Its specifically used most often towards a subject that regards themselves as entitled to a particular esteem or honor and feeling unquestionable is certainly an example of such a case.
References to "high horses" could work, but tend to invoke connotations of morality more so than pride.
Myself, I might say he/she needs to be:
"Taken down a peg (or two)"
However, this is suggests a more passive role for the subject, suggesting that it needs to be acted upon, rather than the subject itself carrying the responsibility to act.
Expression such as "get real" or "get a clue" might be commonly be used in the latter sense. Though they are less specific to pride, they are often used in pride-related cases.
There are plenty of ways to describe such a person. You might say they are self-absorbed, self-centered, or think too highly of themselves. However, not many expressions dictate what they should do about it. Likely because not many people have had much success telling them anyway.
Which reminds me of an applicable phrase that my Swedish grandmother would say about my Danish grandfather:
"You can always tell a Dane, but you can't tell him much!"