Zip on handbag regularly splits (4)
I believe the answer is:
nada
'zip' is the definition.
(synonyms)
'on handbag regularly splits' is the wordplay.
'on' is a charade indicator (letters next to each other).
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
'splits' becomes 'n' (I can't justify this - if you can you should believe this answer much more).
The alternating letters of 'handbag' are 'ada'.
'ada' after 'n' is 'NADA'.
Can you help me to learn more?
(Other definitions for nada that I've seen before include "Nothing (US)" , "zip" , "Love" , "Not a sausage" .)