Laugh about Washington's leader — what's he on? (7)
I believe the answer is:
'he on?' is the definition.
Although both the answer and definition are singular nouns, I don't see how they can define each other.
'laugh about washington's leader' is the wordplay.
'laugh' becomes 'titter' (titter is a kind of laugh**).
'about' indicates putting letters inside.
'leader' suggests taking the first letters.
The first letter of 'washingtons' is 'w'.
'titter' placed around 'w' is 'TWITTER'.
'what's' is the link.
(Other definitions for twitter that I've seen before include "Bird's sound; trivial talk" , "Chatter" , "state of excitement" , "Chirrup tremulously" , "(Make) a noise like a bird" .)