The most common and most likely answer to this crossword clue is the 1 plus 3 letter word A BIT
A
B
I
T
More clues leading to the result A BIT
- Rather ordinary course of behaviour hard to drop
- Cockney’s custom? To an extent
- Topless dress? Rather!
- Not much attire, going topless
- Kicking heroin habit for short while
- Nuns’ clothing is non-starter for some
- Even parts of Bambi have it to some extent
- Rather dress stays unopened
- Some uninhabitable houses
- Rather the thing for Cockney monk to wear?
Buddy explains!

The straight part
We know that "short while" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case short while = a bit.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.