Town east of Glasgow, centre of coiffure equipment? (7)

I believe the answer is:

airdrie

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'town' is the definition.
(I have seen 'Scottish town' mean 'airdrie' so perhaps 'town' could also mean 'airdrie')

I don't understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for airdrie that I've seen before include "North Lanarkshire town" , "Town to E. of Glasgow" , "community up north" , "Burgh E. of Glasgow" , "Scottish town" .)

I've seen this clue in The Independent.

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