Inquisitiveness (9)
I believe the answer is:
curiosity
'inquisitiveness' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for curiosity that I've seen before include "Something unusual (that killed the cat?)" , "Killer of pet" , "Inquisitiveness" , "25 28 [MARS LANDER]" , "Killer of cat" .)