Regularly chastise pets (4)

I believe the answer is:

cats

'pets' is the definition.
(cat is a type of pet)

'regularly chastise' is the wordplay.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
The alternating letters of 'chastise' are 'CATS'.

(Other definitions for cats that I've seen before include "Siamese, Persian etc" , "Popular musical" , "Musical from TS Eliot" , "Musical; jazz fans" , "Musical (felines?)" .)

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

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