The most common and most likely answer to this crossword clue is the 8 letter word SHRIVELS
I've seen this crossword clue in The Daily Telegraph
S
H
R
I
V
E
L
S
Buddy explains!

The straight part
We know that "dries up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dries up = shrivels.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 SHRIVELS mean?
SHRIVELS verb- To collapse inward; to crumble.
- To become wrinkled.
- To draw into wrinkles.