British agent has an untidy hair style (4)

I believe the answer is:

shag

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'style' is the definition.
(I know that shag is a style)

'british agent has' is the wordplay.
'has' indicates a hidden word.
'SHAG' is hidden in the letters of 'british agent'.

'an untidy hair' is the link.
This may not be right. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for shag that I've seen before include "flighty creature" , "Kind of cormorant - tobacco" , "Diver" , "Coarse tobacco - cormorant" , "Bird - dance" .)

I've seen this clue in The Irish Times.

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