Cheaper attire falling apart after short time (7)

I believe the answer is:

tattier

'cheaper' is the definition.
('tatty' can be a synonym of 'cheap')

'attire falling apart after short time' is the wordplay.
'falling apart' indicates an anagram.
'after' is a charade indicator (letters next to each other).
'short time' becomes 't' (abbreviation for time**).
'attire' with letters rearranged gives 'attier'.
'attier' after 't' is 'TATTIER'.

(Another definition for tattier that I've seen is " More shabby".)

I've seen this clue in The Telegraph.

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