Current rent (3)

I believe the answer is:

rip

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'rent' is the definition.
(rent can mean a tear in something)

I cannot understand how the rest of the clue works.

(Other definitions for rip that I've seen before include "Letters for the deceased" , "Letters often seen on gravestones" , "comment on one passing" , "dissolute character" , "Rest in peace" .)

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

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