Projects one's personality over questionable date with Simon (9)
I believe the answer is:
dominates
'projects one's personality over' is the definition.
'questionable date with simon' is the wordplay.
'questionable' is an anagram indicator.
'with' says to put letters next to each other.
'date' put after 'simon' is 'simondate'.
'simondate' with letters rearranged gives 'DOMINATES'.
(Other definitions for dominates that I've seen before include "Prevails" , "Towers over in Maidstone" , "Is top dog in Maidstone" , "Adopts a masterful attitude" , "Controls" .)