Reckless injunction to keep increasing the rent (8)

I believe the answer is:

tearaway

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'reckless' is the definition.
(I've seen this before)

I don't understand the rest of the clue.

(Other definitions for tearaway that I've seen before include "Might I stir" , "Delinquent" , "reckless type" , "A tough" , "Unruly youth" .)

I've seen this clue in The Telegraph and The Globe and Mail.

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