Giggle about W being X's predecessor (7)
I believe the answer is:
'giggle' is the definition.
(thesaurus)
'about w being x's predecessor' is the wordplay.
'about' is an insertion indicator.
'being x's predecessor' becomes 'titter' (I am not sure about this - if you are sure you should believe this answer much more).
'w' inserted inside 'titter' is 'TWITTER'.
Can you help me to learn more?
(Other definitions for twitter that I've seen before include "Chirping (could be electronic!)" , "Chirpy social website" , "Make high-pitched sounds, as of birds" , "social network site revealed" , "Chirrup tremulously" .)