The most common and most likely answer to this crossword clue is the 4 letter word VAIR
V
A
I
R
Buddy explains!
The straight part
We know that "Cheap fur" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cheap fur = vair.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 VAIR mean?
VAIR noun- A type of fur from a squirrel with a black back and white belly, much used on garments in the Middle Ages.
- An heraldic fur formed by a regular tessellation of bell shapes in two colours, (for example in the image, blue and white).