Steal broken roof covering (5)

I believe the answer is:

slate

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'roof covering' is the definition.
'slate' can be an answer for 'roof' (slating is a kind of roofing). I am not certain of the 'covering' bit.

'steal broken' is the wordplay.
'broken' indicates anagramming the letters.
'steal' is an anagram of 'SLATE'.

Can you help me to learn more?

(Other definitions for slate that I've seen before include "Blast" , "Grey stone; tab" , "Run down" , "rock used in building" , "A roof-tile; criticise heavily" .)

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

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