King Edward possibly suppressing odd bits of talk and gossip (7)
I believe the answer is:
tattler
'gossip' is the definition.
(I know that tattler is a type of gossip)
'king edward possibly suppressing odd bits of talk' is the wordplay.
'king edward possibly' becomes 'tater' (King Edward is a type of potato).
'suppressing' is an insertion indicator.
'odd bits of' means one should take alternating letters.
The alternate letters of 'talk' are 'tl'.
'tater' going around 'tl' is 'TATTLER'.
'and' acts as a link.
(Other definitions for tattler that I've seen before include "One who gossips" , "Chatterer" , "gossip" .)