The most common and most likely answer to this crossword clue is the 4 letter word NAPE
I've seen this crossword clue in The Times
N
A
P
E
More clues leading to the result NAPE
- Seize European scruff
- Part of the neck of northern primate
- Scruff in Suffolk village refused introduction
- Scruff last in line put on fluffy coat
- Scruff's threads close to threadbare
- Casually sleep with English scruff
- Scruff last to gamble on tipster’s choice
- New primate has some neck!
- Some urchin, a perfect scruff
- Scruff takes ecstasy, seeing little sleep ahead
Buddy explains!

The straight part
We know that "Part of the neck" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case part of the neck = nape.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 NAPE mean?
NAPE noun- The back part of the neck.
- The part of a fish or bird immediately behind the head.
- A tablecloth.
- Napalm.
- To bombard with napalm.