Daily show on Queen personality (9)
I believe the answer is:
character
'personality' is the definition.
(I've seen this before)
'daily show on queen' is the wordplay.
'daily' becomes 'char' (I've seen this before).
'show' becomes 'act' (act is a kind of show**).
'on' means one lot of letters go next to another.
'queen' becomes 'er' (abbreviation for Elizabeth Regina).
'char'+'act'+'er'='CHARACTER'
(Other definitions for character that I've seen before include "Letter or figure" , "Role - nature" , "crank" , "Eccentric person" , "Distinctive nature" .)