Regularly chastise gossips (4)
I believe the answer is:
cats
'gossips' is the definition.
(cat is a kind of gossip)
'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 "Popular musical" , "Pets - musical" , "Spectacular Llyod Webber feline musical" , "Some 6 Downs" , "Musical from TS Eliot" .)