Sue gets winter coat dirty (7)

I believe the answer is:

begrime

'dirty' is the definition.
(I know that dirty can be written as begrime)

'sue gets winter coat' is the wordplay.
'sue' becomes 'beg' (I've seen this in another clue).
'gets' is a charade indicator (letters next to each other).
'winter coat' becomes 'rime' (I've seen this in another clue).
'beg'+'rime'='BEGRIME'

I've seen this clue in the Sydney Morning Herald.

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