Peculiar; inquisitive (7)
I believe the answer is:
curious
This clue is a double definition.
'peculiar' is the first definition.
(I know that peculiar can be written as curious)
'inquisitive' is the second definition.
(synonyms)
(Other definitions for curious that I've seen before include "Odd or eager to know" , "Eager to know something, perhaps nosy" , "with a great deal of interest!" , "Strange - inquisitive" , "Unusual; eager to learn" .)