Device that’s arresting the curling (12)

I believe the answer is:

straightener

'device' is the definition.
(device used to straighten hair)

'arresting the curling' is the wordplay.
'curling' is an anagram indicator (letters curl and twist out of order).
'arresting'+'the'='arrestingthe'
'arrestingthe' is an anagram of 'STRAIGHTENER'.

'that's' acts as a link.

I've seen this clue in The Hindu.

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