The most common and most likely answer to this crossword clue is the 4 letter word WHIM
I've seen this crossword clue in The Sunday Telegraph
W
H
I
M
More clues leading to the result WHIM
- Fancy wife? Not her
- Urge that man to chase wife
- Fancy wife overlooking that man!
- Fancy wife and that man getting together
- Fancy woman seen with that bloke
- Fancy being with that man
- Fancy man in particular supporting wife
- Fancy greeting retained by western male
- Fancy that guy burdened with wife
- Fancy a week with that guy?
Buddy explains!

The straight part
We know that "Fancy" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fancy = whim.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 WHIM mean?
WHIM noun- A fanciful impulse, or whimsical idea
- A large capstan or vertical drum turned by horse power or steam power, for raising ore or water, etc., from mines, or for other purposes
- To be seized with a whim; to be capricious.
- A bird, the Eurasian wigeon.