expression, suru verb (irregular)
act important; swagger; put on airs
Idiomatic expression describing someone who behaves as if they are more important or influential than they really are, often with a negative or mocking tone.
彼は新入りなのに、もう大きな顔をしている。
Even though he's a newcomer, he's already acting like he's important.
そんな小さな成功で大きな顔をするな。
Don't swagger around just because of such a small success.