Inquisitive? How strange! (7)
I believe the answer is:
curious
This clue is a double definition.
'inquisitive?' is the first definition.
('curious' can be similar in meaning to 'inquisitive')
'strange' is the second definition.
(similar in meaning)
'how' is the link.
(Other definitions for curious that I've seen before include "Odd, peculiar" , "Strange, unusual" , "Questioning" , "Keen to learn" , "Odd - inquisitive" .)