A ripping thing to do when you're in a hurry (4)

I believe the answer is:

tear

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'a hurry' is the definition.
(tear is a kind of hurry)

I cannot understand how the rest of the clue works.

(Other definitions for tear that I've seen before include "Droplet from the eye" , "Product of the lachrymal gland" , "Droplet; rip" , "A rip and a sign of sadness" , "Rip - eye moisture" .)

I've seen this clue in the Evening Standard.

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