The most common and most likely answer to this crossword clue is the 4 letter word LINT
L
I
N
T
Buddy explains!

The straight part
We know that "dressing" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dressing = lint.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 LINT mean?
LINT noun- A fine material made by scraping cotton or linen cloth; used for dressing wounds.
- Clinging fuzzy fluff that clings to fabric or accumulates in one's pockets or navel etc.
- The fibrous coat of thick hairs covering the seeds of the cotton plant.
- Raw cotton ready for baling.
- To perform a static check on (source code) to detect stylistic or programmatic errors.