"hunger after" is correct and usable in written English.
It is an idiom that means to be eager for or to have a strong desire for something. For example, "He hungered after success and fame all his life."
We hunger after the otherworldly.
Today's fans hunger after a memory of something that never really existed in the first place.
"People feel estranged from political candidates, and they hunger after knowledge about them," he said.
Like zombies, we are never satisfied and hunger after the next "meal".
That means paying attention to sensations of hunger and satiety — the reduction of appetite and/or hunger after eating.
He answered, rather casually, that he understood their hunger, after so many years of humiliation, for revenge.
Some of the pleasures of hiking are compensatory -- rest after exertion, food after hunger, showers after sweat -- but some are objective.
"We are living amid filth and hunger and thirst after a catastrophe".
In the Beatitudes, Jesus blesses those who hunger and thirst after justice.
When slaked, they fall back, crimson mouths agape, and the camera hungers after them.
But this is not the Vince Vaughn-Ben Stiller comedy that was so ardently hungered after.
