Move hastily, thus damage (4)

I believe the answer is:

tear

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This clue could be a double definition.

'move' is the first definition.
(tear is a kind of move)

'hastily thus damage' is the second definition.
'tear' can be an answer for 'damage' (thesaurus). I am not sure about the 'hastily thus' bit.

Can you help me to learn more?

(Other definitions for tear that I've seen before include "A drop of optical moisture" , "Lacerate - sign of sorrow" , "Rip, sever roughly" , "Optical sign of sorrow" , "Secretion of the lacrymal glands" .)

I've seen this clue in the Evening Standard.

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