The most common and most likely answer to this crossword clue is the 8 letter word STICKING
I've seen this crossword clue in The Daily Telegraph
S
T
I
C
K
I
N
G
Buddy explains!

The straight part
We know that "first-aid item" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case first-aid item = sticking.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 STICKING mean?
STICKING verb- To cut a piece of wood to be the stick member of a cope-and-stick joint.
- To compose; to set, or arrange, in a composing stick.
- To furnish or set with sticks.
- To become or remain attached; to adhere.
- To jam; to stop moving.
- To tolerate, to endure, to stick with.
- To persist.
- Of snow, to remain frozen on landing.
- To remain loyal; to remain firm.
- To hesitate, to be reluctant; to refuse (in negative phrases).
- To be puzzled (at something), have difficulty understanding.
- To cause difficulties, scruples, or hesitation.
- To attach with glue or as if by gluing.
- To place, set down (quickly or carelessly).
- To press (something with a sharp point) into something else.
- To fix on a pointed instrument; to impale.
- To adorn or deck with things fastened on as by piercing.
- To perform (a landing) perfectly.
- To propagate plants by cuttings.
- (joinery) To run or plane (mouldings) in a machine, in contradistinction to working them by hand. Such mouldings are said to be stuck.
- To bring to a halt; to stymie; to puzzle.
- To impose upon; to compel to pay; sometimes, to cheat.
- To have sexual intercourse with.
- To stand pat: to cease taking any more cards and finalize one's hand.
- A sequence or arrangement of drum notes to be played with drumsticks.