Crossword Genius

Diplomat dealing with bushy hirsute growth? (7)

Ross

I believe the answer is:

attache

I'm a little stuck... Click here to teach me more about this clue!

'diplomat' is the definition.
(I know that attache is a type of diplomat)

'dealing with bushy hirsute growth?' is the wordplay.
I cannot quite understand how this works, but
'growth?' could be 'tache' (short for moustache) and 'tache' is found in the answer.
'dealing with' could be 'at' (eg looking at something) and 'at' is found within the answer.
No letters remain.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for attache that I've seen before include "Specialised envoy" , "Junior official" , "Embassy worker" , "This small rectangular case carries documents" , "Connected to the French" .)

I've seen this clue in The Times.
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