Mull over, with "on" (4)
I believe the answer is:
chew
'mull over with on' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for chew that I've seen before include "bit of tobacco" , "Masticate, grind between teeth" , "Gnaw" , "work with canines" , "Bite repeatedly" .)