The most common and most likely answer to this crossword clue is the 8 letter word DIFFUSER
I've seen this crossword clue in Financial Times
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More clues leading to the result DIFFUSER
Buddy explains!

The straight part
We know that "hairdryer attachment" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case hairdryer attachment = diffuser.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 DIFFUSER mean?
DIFFUSER noun- Any person or thing that diffuses.
- A device designed to diffuse a scent efficiently.
- Any device that or spreads out or scatters light, making the light appear softer.
- A shaped section of a car's underbody which improves the car's aerodynamic properties.
- A mechanical device that is designed to control the characteristics of a fluid at the entrance to a thermodynamic open system.
- (sewage treatment) An aerating device consisting of a membrane with fine pores, through which air is blown to generate small bubbles.
- A cooking item that can be placed above a stove heating element or burner to separate the cooking utensil from the heat source.
- A hairdryer attachment that diffuses the flow of air.