The most common and most likely answer to this crossword clue is the 8 letter word YEARNING
I've seen this crossword clue in The Guardian
Y
E
A
R
N
I
N
G
More clues leading to the result YEARNING
- Deep desire to be studying with new head
- Desire of head changing study
- Year before getting paid results in hunger
- Desire unknown quantity, being paid
- Hunger may be variable before making money
- Yankee being paid in yen
- Yen — yen! Making money
- Desire 12 months at home? No good hiding that
- Desire new head to lead study
- Fancy cutting wages after the end of July
Buddy explains!

The straight part
We know that "hunger" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case hunger = yearning.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does YEARNING mean?
YEARNING verb- To long, have a strong desire (for something).
- To long for something in the past with melancholy, nostalgically.
- To have strong feelings of love, sympathy, affection, etc. (toward someone).
- To be pained or distressed; to grieve; to mourn.
- To pain; to grieve; to vex.
- To curdle, as milk.
- A wistful or melancholy longing.
- Rennet (an enzyme to curdle milk in order to make cheese).