Rat leaves with cat (5)

I believe the answer is:

retch

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'cat' is the definition.
(I know that cat can be written as retch)

I don't understand the remainder of the clue.

(Other definitions for retch that I've seen before include "Unsuccessful effort to vomit" , "Try to bring up" , "Try to be sick" , "Sound and seem to vomit" , "throw up" .)

I've seen this clue in The Sunday Times and The Times.

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