The most common and most likely answer to this crossword clue is the 7 letter word WHITTLE
I've seen this crossword clue in The Times
W
H
I
T
T
L
E
Buddy explains!

The straight part
We know that "Shave" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case shave = whittle.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 WHITTLE mean?
WHITTLE noun- A knife; especially, a pocket knife, sheath knife, or clasp knife.
- To cut or shape wood with a knife.
- To reduce or gradually eliminate something (such as a debt).
- To make eager or excited; to excite with liquor; to inebriate.
- A coarse greyish double blanket worn by countrywomen, in the west of England, over the shoulders, like a cloak or shawl.
- A whittle shawl; a kind of fine woollen shawl, originally and especially a white one.