This turned up in The Masks of Time, a 1968 SF novel by Robert Silverberg I was re-reading recently: “I had seen his colossal esurience, his imperial self-indulgence, his gargantuan appetite for sensual pleasure of all sorts.”
It comes from Latin esurire, to be hungry, derived from edere, to eat (and so is a cousin of edacious and esculent. It means hunger or appetite. It’s rare. However, its linked adjective esurient is more common, though it’s hardly an everyday word. Both can be used literally, though when they are they’re often intended humorously or to imply excessive indulgence, as here:
She is proportioned like a well-upholstered Hottentot in consequence of her perpetual esurience.
Independent on Sunday, 17 Jun. 2007.
Fans of the cheese shop sketch from the BBC TV comedy Monty Python’s Flying Circus will recall that esurient appeared in it, the only time that many people have ever encountered the word.
However, esurience and esurient are much more likely to refer to figurative hunger, perhaps for power or riches, hence meaning greed:
As a world leader in greenhouse-gas emissions, the United States is woefully behind in curbing its esurient fuel-consumption habits.
The Deseret News, Salt Lake City, Utah, 29 Jul. 2007.