The most common and most likely answer to this crossword clue is the 7 letter word WILLIES
I've seen this crossword clue in The Times
W
I
L
L
I
E
S
Buddy explains!

The straight part
We know that "Fear" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fear = willies.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 WILLIES mean?
WILLIES noun- (with "the") A feeling of nervousness or fear.
- Any of various deciduous trees or shrubs in the genus Salix, in the willow family Salicaceae, found primarily on moist soils in cooler zones in the northern hemisphere.
- The wood of these trees.
- A cricket bat.
- (1800s) The baseball bat.
- A rotating spiked drum used to open and clean cotton heads.
- A willow basket.
- A fish basket.
- (hypocoristic) the penis.
- Term of abuse.
- A person who is manipulated into serving as a useful agent without knowing it.